University of California - Irvine

Department of Mathematics

Professor Emeritus Edriss S. Titi

Mathematics, Mechanical and Aerospace Engineering

 

 

Rowland Hall Building

Room 510C
Irvine, CA 92697-3875 
(949) 824-3156 Office

(949) 407-9877 Mobile
(949) 824-7993 Fax 
etiti@math.uci.edu

                                        

                               

 

PUBLICATIONS

 

(Please contact me at etiti@math.uci.edu for preprints and reprints)
 

RECENT PREPRINTS
(Can be found on the arXiv)

 

M. Lopes Filho, H. Nussenzveig Lopes, E.S. Titi and A. Zang, Convergence of the 2D Euler-α to Euler equations in the Dirichlet case: indifference to boundary layers, (submitted). arXiv:1403.5682

 

H. Bessaih, E. Olson and E.S. Titi, Continuous assimilation of data with stochastic noise, (submitted). arXiv:1406.1533

 

D.A.F. Albanez, H.J. Nussenzveig Lopes and E.S. Titi, Continuous data assimilation for the three-dimensional Navier-Stokes-α model, (submitted).

 

A. Larios and E.S. Titi, Global regularity vs. finite-time singularities: some paradigms on the effect of boundary conditions and certain perturbations, (submitted). arXiv:1401.1534

 

C. Cao, J. Li and E.S. Titi, Global well-posedness for the 3D primitive equations with only horizontal viscosity and diffusion, (submitted). arXiv:1406.1995

 

M.S. Jolly, T. Sadigov and E.S. Titi, A determining form for the damped driven nonlinear Schrödinger equation- Fourier modes case, (submitted). arXiv:1406.2626

 

Q. Jiu, D. Niu, E.S. Titi and Z. Xin, Axisymmetric Euler-α equations without swirl: existence, uniqueness and Radon measure valued solutions, (submitted).


C. Cao, S. Chen and E.S. Titi, A turbulence model for the 1D dispersive wave, (Preprint).

 

 

 

PAPERS TO APPEAR

 

A. Azouani and E.S. Titi, Feedback control of nonlinear dissipative systems by finite determining   parameters - a reaction-diffusion paradigm, Evolution Equations and Control Theory (EECT), (2014), (to appear). arXiv:1301.6992

 

Y. Guo, M A. Rammaha, S. Sakuntasathien, E.S. Titi, D. Toundykov, Hadamard well-posedness for a hyperbolic equation of viscoelasticity with supercritical sources and damping, Journal of Differential Equations, (2014),  (to appear). arXiv:1308.0720

 

M.C. Lopes-Filho, A.L. Mazzucato, D. Niu, H.J. Nussenzveig-Lopes and E.S. Titi, Planar limits of three-dimensional incompressible  flows with helical symmetry, Journal of Dynamics and Differential Equations, (2014), (to appear). arXiv:1304.2082

 

C. Cao, J. Li and E.S. Titi, Local and global well-posedness of strong solutions to the 3D primitive equations with vertical eddy diffusivity, Archive of Analysis and Rational Mechanics, (2014), (to appear). arXiv:1312.6035

 

P. Gérard, Y. Guo and E.S. Titi, On the radius of analyticity of solutions to the cubic Szegö equation, Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire, (in press). http://dx.doi.org/10.1016/j.anihpc.2013.11.001. arXiv:1303.6148

 

C. Cao, S. Ibrahim, K. Nakanishi and E.S. Titi,  Finite-time blowup for the inviscid primitive equations of oceanic and atmospheric dynamic, Communications in Mathematical Physics, (2014), (to appear). arXiv:1210.7337

 

Y. Guo, K. Simon and E.S. Titi, On a nonlinear system of coupled KdV equations, Communications in Mathematical Sciences, (to appear). arXiv:1310.1130

 

C. Cao, J. Li and E.S. Titi, Global well-posedness of strong solutions to the 3D primitive equations with horizontal eddy diffusivity, Journal of Differential Equations, (2014), (to appear). arXiv:1401.1234

 

 

 

 

SELECTED RECENTLY PUBLISHED PROCEEDINGS PAPERS  

 

6. K.Ríos-Soto, C. Castillo-Chavez, M. Neubert, E.S. Titi, A. Yakubu, Epidemic spread in population demographic equilibrium, Proceeding of the Snowbird Conference on Modeling The Dynamics of Human Diseases: Emerging Paradigms and Challenges. Eds. A. Gumel (Chief Editor), C. Castillo-Chavez, D.P. Clemence,  and R.E. Mickens, (2006).

 

5. C. Cao and E. S. Titi, Asymptotic behavior of viscous 1-D scalar conservation laws with Neumann boundary conditions, Third Palestinian Mathematics Conference,  Bethlehem University, West Bank,  Mathematics & Mathematics Education,  S. Elaydi, E. S. Titi,   M. Saleh, S. K. Jain  and  R. Abu Saris, editors, World Scientifc, 2002. pdf

 

4. S. Shvartsman, C. Theodoropoulos, R. Rico-Martinez, I.G. Kevrekidis, E.S. Titi, and T. J. Mountziares, Order reduction of nonlinear dynamic models for distributed reacting systems, Proceedings of DYCOPS-5, Corfou, Greece, June 1997, C. Georgakis, ed., pp.674-681.

 

3. A. Doelman and E.S. Titi, On the exponential rate of convergence of the Galerkin approximation in Ginzburg-Landau equation, Proceedings of the  NATO Advanced Research Workshop: Asymptotic and  Numerical Methods for Partial Differential Equations with  Critical Parameters, M. Garbey and H.G. Kaper, eds., Kluwer Academic Publishers,  Dordrecht, 1993, pp. 241-252.

 

2. A. Bloch and E.S. Titi, On the dynamics of rotating elastic beams, Proceedings of: New Trends in Systems Theory, July 9-11, 1990, Genoa, Italy: G. Conte, A.M. Perdon and B. Wyman, eds., Birkhäuser, Boston, Basel, Berlin.

 

1. H.S. Brown, M.S. Jolly and I.G. Kevrekidis and E.S. Titi, Use of approximate inertial manifolds in bifurcation calculations, Proceedings of NATO Advanced Research Workshop on: Continuation and Bifurcations :  Numerical Techniques and Applications,  September 18 - 22, 1989, Belgium, D. Roose et al. (eds.), pp. 9-23, Kluwer Academic Publishers.

 

 

 

SELECTED RECENTLY PUBLISHED JOURNAL PAPERS

 

154. C. Cao, A. Farhat and E.S. Titi, Global regularity for an inviscid three-dimensional slow limiting ocean dynamics model, Communications in Information and Systems (CIS), 13(1) (2013), 97-122. (An invited article for a special issue in honor of Professor Marshall Slemrod on the occasion of his 70th birthday). arXiv:1311.6064

 

152. A. Biswas, M.S. Jolly, V. Martinez and Edriss S. Titi, Dissipation length scale estimates for turbulent flows - a Wiener algebra approach, Journal of Nonlinear Science, 24 (2014) 441-471. DOI 10.1007/s00332-014-9195-8. arXiv:1310.3496

 

150. C. Foias, M. Jolly, R. Kravchenko and E.S. Titi, A unified approach to determining forms for the 2D Navier-Stokes equations - the general interpolants case, Uspekhi Matematicheskikh Nauk, 69(2) (2014) 177-200; also  Russian Mathematical Surveys, 69(2) (2014) 359-381. (An invite article for a special issue in memory  of Professor Mark Vishik). arXiv:1309.0247

 

148. A. Azouani, E. Olson  and E.S. Titi,  Continuous data assimilation using general interpolant  observables, Journal of Nonlinear Science,  24(2) (2014),  277-304. DOI 10.1007/s00332-013-9189-y. arXiv:1304.0997

 

147. Y. Guo and E.S. Titi, Persistency of analyticity for quasi-linear wave equations: an energy-like approach, Bulletin  of Institute of Mathematics, Academia Sinica (New Series), 8(4) (2013), 445-479. (2013),   (An invite article for a special issue in honor of Professor Neil Trudinger  on the occasion of his 70th birthday). arXiv:1301.0137

 

146. A. Larios, E. Lunasin and E.S. Titi, Global well-posedness for the 2D Boussinesq system with anisotropic  viscosity and without heat diffusion, Journal of Differential Equations, 255 (2013), 2636-2654.

 

144.  J. Lowengrub, E.S. Titi and K. Zhao, Analysis of a mixture model of tumor growth, European Journal of Applied Mathematics, 24 (2013), 691-734.

 

143. C. Bardos, M. Lopes Filho, D. Niu, H. Nussenzveig Lopes and E.S. Titi, Stability of viscous, and instability of non-viscous, 2D weak solutions of incompressible fluids under 3D perturbations, SIAM, Journal on Mathematical Analysis, 45(3) (2013), 1871-1885.

 

142.  L. Biferale and E.S. Titi, On the global regularity of a helical-decimated version of the 3D Navier-Stokes equations, Journal of Statistical Physics, 151 (2013), 1089-1098.

 

141. J.D. Gibbon and E.S. Titi, 3D incompressible Euler with a passive scalar: a road to blow up? Journal of Nonlinear Science, 23(6) (2013), 993-1000. DOI 10.1007/s00332-013-9175-4.

 

140. C. Bardos and E.S. Titi, Mathematics and turbulence: where do we stand? Journal of Turbulence, 14(3) (2013),  42-76.

 

139. A. Larios, E. S. Titi,   Higher-order global regularity of an inviscid Voigt-regularization of the three-dimensional inviscid resistive magnetohydrodynamic equations, Journal of Mathematical Fluid Mechanics, 16 (2014), 59–76. DOI 10.1007/s00021-013-0136-3.  arXiv:1104.0358.

 

138. C. Foias, M. Jolly, R. Kravchenko and E.S. Titi, A determining form for the 2D Navier-Stokes equations - the Fourier modes case,    Journal of Mathematical Physics, 53 (2012), 115623. (An invite article for a special issue in honor of Professor P. Constantin on the occasion of his 60th birthday).

 

137. C.R. Doering, I. Kukavica and E.S. Titi, Introduction to special issue: incompressible fluids, turbulence and mixing, Journal of Mathematical Physics, 53 (2012), 115501.

 

136. C. Cao, A. Farhat and E.S. Titi, Global well-posedness of an inviscid three-dimensional pseudo-Hasegawa-Mima model, Communications in Mathematical Physics, 319(1) (2013), 195-229.

 

135. C. Bardos, E.S. Titi and E. Wiedemann, The vanishing viscosity as a selection principle for the Euler equations: The case of 3D shear flow; La viscosité évanescente comme critère de sélection pour les solutions de l’équation d’Euler: Le cas du flot de cisaillement,   Comptes Rendus De L'Académie Des Sciences, Paris,  Série I, Mathématique, 350(15) (2012), 757-760.

 

134. A. Farhat, L. Panetta, E.S. Titi and M.B. Ziane, Long-time behavior of a two-layer model of baroclinic quasi-geostrophic turbulence, Journal of Mathematical Physics, 53  (2012), 115603. (An invite article for a special issue in honor of Professor P. Constantin on the occasion of his 60th birthday).

 

133. C. Cao and E.S. Titi, Global well-posedness of the three-dimensional stratified primitive equations with partial vertical mixing turbulence diffusion, Communications in Mathematical Physics, 310 (2012), 537-568.

 

132. K. Hayden, E. Olson and E.S. Titi, Discrete data assimilation in the Lorenz and 2D Navier–Stokes equations, Physica D, 240 (2011), 1416-1425.

 

131. Z. Artstein, C.W. Gear, I.G. Kevrekidis, M. Slemrod and E.S. Titi, Analysis and computation of a discrete KdV-Burgers type equation with fast dispersion and slow diffusion, SIAM Journal on Numerical Analysis, 49(5) (2011), 2124-2143.

 

130. A.V. Babin, A.A. Ilyin, and E.S. Titi, On the regularization mechanism for the spatially periodic Korteweg-de Vries equation, Communications in Pure and Applied Mathematics, 64 (2011), 591-648.

 

129. C. Cao and E.S. Titi, Global  regularity criterion  for the 3D  Navier-Stokes equations involving one entry of the velocity gradient tensor,  Archive of Rational Mechanics & Analysis, 202  (2011), 919-932.

 

128. H. Bessaih, F. Flandoli and E.S. Titi, Stochastic attractors for shell phenomenological models of turbulence, Journal of Statistical Physics, 140 (2010), 688-717.

 

127. F. Ramos and E.S. Titi, Invariant measures for the 3D Navier-Stokes-Voigt equations and their Navier-Stokes limit, Discrete and Continuous Dynamical Systems, 28(1) (2010), 375-403. (An invite article for a special issue in honor of Professor R. Temam on the occasion of his 70th birthday).

 

126. A. Larios and E.S. Titi, On the higher-order global regularity of the  inviscid Voigt-regularization of three-dimensional hydrodynamic models, Discrete and Continuous Dynamical Systems, 14(2) (2010), 603-627. (An invite article for a special issue in honor of Professor P. Kloeden on the occasion of his 60th birthday).

 

125.  J. Linshiz and E.S. Titi, On the convergence rate of the Euler-α,inviscid second-grade fluid, model to the Euler equations, Journal of Statistical Physics, 138(1) (2010), 305-332.

 

124. C. Bardos and E.S. Titi, Loss of smoothness and energy conserving rough weak solutions for the 3d Euler equations, Discrete and Continuous Dynamical Systems, Series S, 3(2) (2010), 185-197. (An invite article for a special issue on honor of Professor V. Solonnikov in the occasion of his 75th birthday).

 

123. Y. Cao and E.S. Titi, On the rate of convergence of  the two-dimensional α-models of turbulence to the Navier-Stokes equations, Numerical Functional Analysis and Optimization, 30(11&12) (2009), 1231-1271.

 

122. C. Bardos, J. Linshiz and E.S. Titi, Global regularity and convergence of a Birkhoff-Rott-α approximation of the dynamics of vortex sheets of the 2D Euler equations, Communications in Pure and Applied Mathematics, 63(6)  (2010), 697-746.

 

121. V.K. Kalantarov and E.S. Titi, Global attractors and determining modes for the 3D Navier-Stokes-Voight equations, Chinese Annals of Mathematics, Series B, 30(6) (2009), 697-714. (An invited article for a special issue in honor of Professor A. Majda on the occasion of his 60th birthday).

 

120. C. Bardos, U. Frisch, W. Pauls, S.S. Ray, and E.S. Titi, Entire solutions of hydrodynamical equations with exponential dissipation, Communications in Mathematical Physics, 293 (2010), 519-543.

 

119. B. Levant, F. Ramos and E.S. Titi, On the statistical properties of the 3D incompressible Navier-Stokes-Voigt model, Communications in Mathematical Sciences, 8(1) (2010), 277-293.  (An invite article for a special issue in honor of Professor A. Majda in the occasion of his 60th birthday).

 

118. A.-C. Bennis, R. Lewandowski and E.S. Titi, Simulations de l'écoulement turbulent marin ave un modéle de déeconvolution, Comptes Rendus De L'Académie Des Sciences, Paris, Série I,  347 (2009), 445-450.

 

117. Y. Cao, Z.H. Musslimani and E.S. Titi, Modulation theory for self-focusing in the nonlinear Schrödinger-Helmholtz equation, Numerical Functional Analysis and Optimization, 30 (2009), 46-69.

 

116. B. Ettinger and E.S. Titi, Global existence and uniqueness of weak solutions of 3-D Euler equations with helical symmetry in the absence of vorticity stretching, SIAM, Journal on Mathematical Analysis, 41(1) (2009), 269–296.

 

115. V.K. Kalantarov, B. Levant and E.S. Titi, Gevrey regularity of the global attractor of the 3D Navier-Stokes-Voight equations, Journal of Nonlinear Science, 19 (2009), 133-152.

 

114. C. Cao and E.S. Titi, Regularity criteria for the three-dimensional Navier-Stokes equations, Indiana University Mathematics Journal, 57(6) (2008), 2643-2662. (An invite article for a special issue in honor of Professor C. Foias in the occasion of his 75th birthday).

 

113. E. Olson and E.S. Titi, Determining modes and Grashoff number in 2D turbulence – A numerical case study, Theoretical and Computational Fluid Dynamics, 22(5) (2008), 327-339.

 

112. B.J. Geurts, A. Kuczaj and E.S. Titi, Regularization modeling for large-eddy simulation of homogeneous isotropic decaying turbulence, Journal of Physics A, 41 (2008), 344008 (29pp). (An invite article for a special issue in honor of Professor D.D. Holm in the occasion of his 60th birthday).

 

111. Y. Cao, Z.H. Musslimani and E.S. Titi, Nonlinear Schrödinger-Helmholtz equation as numerical regularization of the nonlinear Schrödinger equation, Nonlinearity, 21 (2008), 879-898.

 

110. E. Lunasin, S. Kurien and E.S. Titi, Spectral scaling of α-models for two-dimensional turbulence, Journal of Physics A, 41 (2008), 344014 (10pp). (An invite article for a special issue in honor of Professor D.D. Holm in the occasion of his 60th birthday).

 

109. G. Katriel, R. Kupferman and E.S. Titi, Long-time limit for a class of quadratic infinite-dimensional dynamical systems inspired by models of viscoelastic fluids, Journal of Differential Equations, 245 (2008), 2771-2784.

 

108. C. Bardos, J. Linshiz and E.S. Titi, Global regularity for a Birkhoff-Rott-α approximation of the dynamics of vortex sheets of the 2D Euler equations, Invited article in the occasion of 250 years for the Euler Equations, Physica D, 237 (2008) 1905-1911. An invited article for a special issue in the occasion of 250 years for the Euler Equations.

 

107. Z. Artstein, J. Linshiz and E.S. Titi, Young measure approach to computing slowly advancing fast oscillations, SIAM, Multiscale Modeling and Simulation,  6(4) (2007), 1085-1097.

 

106. R. Kupferman, C. Mangoubi and E.S. Titi, A Beale-Kato-Majda breakdown criterion for an Oldroyd-B fluid in the creeping flow regime, Communications in Mathematical Sciences,  6(1) (2008), 235-256.

 

105. Z. Artstein, I.G. Kevrekidis, M. Slemrod and E.S. Titi, Slow observables of singularly perturbed differential equations, Nonlinearity, 20 (2007), 2463-2481.

 

104. V.V. Chepyzhov, E.S. Titi, and M.I. Vishik, On convergence of trajectory attractors of 3D Navier--Stokes-α model as α approaches 0, Matematicheskii Sbornik,  198:12 (2007), 3-36.

 

103. C. Bardos and E.S. Titi, Euler equations of incompressible ideal fluids, Uspekhi Matematicheskikh Nauk, UMN 62:3(375) (2007), 5-46. Also in Russian Mathematical Surveys, 62(3) (2007), 409-451.

 

102. E.M. Lunasin, S. Kurien, M. Taylor and E.S. Titi, A study of the Navier-Stokes-α model for two-dimensional turbulence, Journal of Turbulence, 8(1) (2007), 1-21.

 

101. R. Benzi, B. Levant, I. Procaccia and E.S. Titi, Statistical properties of nonlinear shell models of turbulence from linear advection models: rigorous results, Nonlinearity, 20(6) (2007), 1431-1443.

 

100. B. Khouider and E.S. Titi, An inviscid regularization for the surface quasi-geostrophic equation, Communications in Pure and Applied Mathematics, 61(10) (2008), 1331-1346.

 

99. C. Cao , J. Qin and E.S. Titi, Regularity criterion for solutions of three-dimensional turbulent channel flows, Communications in Partial Differential Equations,  33(1-3) (2008), 419-428.

 

98. P. Constantin, B. Levant and E.S. Titi, Sharp lower bounds for the dimension of the global attractor of the Sabra shell model of turbulence, Journal of Statistical Physics, 127(6) (2007), 1173-1192.

 

97. A.A. Ilyin and E.S. Titi, On the domain of analyticity and small scales for the solutions of the damped-driven 2D Navier-Stokes equations, Dynamics of Partial Differential Equations, 4(2) (2007), 111-127.

 

96. P. Constantin, B. Levant and E.S. Titi, A note on the regularity of inviscid shell model of turbulence, Physics Review E, 75 (2007), 016304.

 

95. Y. Cao, E.M. Lunasin and E.S. Titi, Global well-posedness of three-dimensional viscous and inviscid simplified Bardina turbulence models, Communications in Mathematical Sciences, 4(4) (2006), 823-84.

 

94. P. Constantin, C. Fefferman, E.S. Titi and  A. Zarnescu, Regularity of coupled two-dimensional Nonlinear Fokker-Planck and Navier-Stokes Systems, Communications in Mathematical Physics, 270(3)  (2007), 789-812.

 

93. J. Linshiz and E.S. Titi, Analytical study of certain magnetohydrodynamics-α models, Journal of Mathematical Physics, 48 (2007), 065504.

 

92. S.I. Chernyshenko, P. Constantin, J.C. Robinson and  E.S. Titi,  A posteriori regularity of the three-dimensional Navier-Stokes equations from numerical computations, Journal of Mathematical Physics, 48 (2007), 065204.

 

91. Y. Cao and E.S. Titi, Trivial stationary solutions to the Kuramoto-Sivashinsky and certain nonlinear elliptic equations, Journal of Differential Equations, 231 (2006), 755-767.

 

90. A.A. Ilyin and E.S. Titi, The damped-driven 2D Navier-Stokes system on large elongated domains, Journal of Mathematical Fluid Mechanics, 10(2) (2007), 159-175.

 

89. V.V. Chepyzhov, E.S. Titi, and M.I. Vishik,  On the convergence of solutions of the Leray-α model to the trajectory attractor of the 3D Navier-Stokes system, Journal of Discrete and Continuous Dynamical Systems - Serie A, 17(3) (2007), 33-52.

 

88. P. Constantin, B. Levant,  E.S. Titi, Analytic study of shell models of turbulence, Physica D,  219(2) (2006), 120-141.

 

87. E. Olson and E.S. Titi, Viscosity versus vorticity stretching: global well-posedness for a family of the Navier-Stokes alpha-like models, Nonlinear Analysis Series A: Theory Methods, 66(11) (2007), 2427-2458.

 

86. A.A.  Ilyin, E.M. Lunasin and E.S. Titi, A modified-Leray-α sub-grid scale model of turbulence, Nonlinearity, 19 (2006), 879-897.

 

85. C. Cao and E.S. Titi, Global well-posedness of the three-dimensional viscous primitive equations of large scale ocean and atmosphere dynamics, Annals of Mathematics, 166(1) (2007), 245-267.

 

84. A.A. Ilyin and E.S. Titi, Sharp estimates for the number of  degrees of freedom for the damped-driven 2D Navier-Stokes equations, Journal of Nonlinear Science, 16(3) (2006), 233-253.

 

83. D. Holm and E.S. Titi, Computational models of Turbulence: The LANS-α model and the role of global analysis, Feature Article: SIAM News, 38(7), September 2005.

 

82. J.D. Gibbon and E.S. Titi, Cluster formation in complex multi-scale systems,  Royal Society London,  Proceedings, Series A, Mathematical, Physical & Engineering Sciences, 461 (2005), 3089-3097.

 

80. P. Constantin, E. S. Titi and J. Vukadinovic, Dissipativity and Gevrey regularity of a Smoluchowski  equation, Indiana University Mathematics Journal, 54(4) (2005), 949-970.

 

79. A. Ilyin, A. Miranville and E. S. Titi, Small viscosity sharp estimates for the global attractor of the 2-D damped-driven Navier--Stokes equations, Communications in Mathematical Sciences,  2(3) (2004),  403-426.

 

78. A. Cheskidov, D. D. Holm, E. Olson and E. S. Titi, On a Leray-α Model of Turbulence, Royal Society London,  Proceedings,  Series A,   Mathematical, Physical & Engineering Sciences, 461 (2005),  629-649.

 

77. C. Cao, E.S. Titi and M. Ziane, Ahorizontal” hyper--diffusion 3-D thermocline planetary geostrophic model:  well-posedness and long time behavior , Nonlinearity, 17 (2004),  1749-1776.

 

76. M. I. Vishik, E. S. Titi and V.V.Chepyzhov, Trajectory attractor approximations of the 3D Navier-Stokes system by a Leray-α model, Russian Mathematical Dokladi (Translated from Russian),  71 (2005), 92-95.

 

75. P. Constantin, I. G. Kevrekidis and E. S. Titi , Asymptotic States of a Smoluchowski Equation , Archive of Rational Mechanics and Analysis,  174(3) (2004), 365-384.

 

74. C. Cao, D. Holm and E.S. Titi, Traveling wave solutions for  a class of one-dimensional nonlinear shallow water  wave models, Journal of Dynamics and Differential Equations,  16(1) (2004), 167-178.

 

73. A.A. Ilyin and E.S. Titi, Attractors to the two-dimensional Navier-Stokes-α model: An alpha-dependence study, Journal of Dynamics and Differential Equations, 15 (2003), 751-777.

 

72. H. Bellout, S. Benachour and E.S. Titi, Finite-time singularity versus global regularity for hyperviscous Hamilton-Jabcobi-like equations, Nonlinearity, 16 (2003), 1967-1989.

 

71. P. Constantin, I. Kevrekidis and E.S. Titi, Remarks on a Smoluchowski equation, Discrete and Continuous Dynamical Systems, 11 (2004), 101-112.

 

70. E. Olson and E.S. Titi, Determining modes for continuous data assimilation in 2-D turbulence, Journal of Statistical Physics, 113 (2003), 799-840.

 

69. L. Margolin, E.S. Titi  and S. Wynne, The postprocessing Galerkin and nonlinear Galerkin methods - a truncation analysis point of view,  SIAM, Journal of Numerical Analysis, 41 (2003), 695-714.

 

68. Y. Chung and E. S. Titi, Inertial manifolds and Gevrey regularity for the Moore-Greitzer model of turbo-machine engine, Journal of Nonlinear Science, 13 (2003), 1-26.

 

67. C. Cao and E. S. Titi, Global well-posedness and finite dimesional global attractor for a 3-D planetary geostrophic viscous model, Communications in Pure and Applied Mathematics, 56 (2003), 198-233.

 

66. P.G. Kevrekidis, I. G. Kevrekidis, A. R. Bishop and E. S. Titi, A continum approach to discreteness, Physical Review E, 65 (2002), no. 4, 046613.

 

65.  C. Cao, I. Kevrekidis and E.S. Titi, Numerical criterion for the stabilization of steady states of the   Navier-Stokes equations, Indiana University Mathematics Journal,  50 (2001), 37-96. (A special Issue in Honor of C. Foias and R. Temam).

 

64. C. Foias, D. Holm and E.S. Titi, The three-dimensional viscous Camassa-Holm equations and their relation to the Navier-Stokes equations and turbulence theory, Journal of Dynamics and Differential Equations, 14 (2002), 1-35.

 

63.  C. Foias, I.  Kukavica, M. Jolly and E.S. Titi, The Lorenz equations as a metaphore for the Navier-Stokes equations, Discrete and Continuous Dynamical Systems, 7 (2001), 403-429.

 

62. C. Foias, D. Holm and E.S. Titi, The Navier-Stokes-alpha model of fluid turbulence, Physica D, 152 (2001), 505-519. (Special  Issue in Honor of V.  E. Zakharov on the Occasion of His 60th Birthday).

 

61.  M. Oliver and E.S. Titi, On the domain of spatial analyticity for solutions of  second order nonlinear analytic parabolic and elliptic  differential equations,  Journal of Differential Equations, 174 (2001), 55-74.

 

60. J. Novo, E.S.Titi and S. Wynne, Efficient methods using high accuracy approximate inertial manifolds, Numerische Mathematik, 87 (2001), 523-554.

 

59. B. García-Archilla, J. Novo and E.S. Titi, Postprocessing Fourier spectral methods:  the case of smooth solutions, Applied Numerical Mathematics, 43 (2002), 191-209.

 

58.   M. Oliver and E.S. Titi, Remark on the decay rate of higher order derivatives of solutions to the Navier-Stokes equations in  Rⁿ,  Journal of Functional Analysis, 172 (2000),  1-18.

 

57. M. Oliver and E.S. Titi, Gevrey regularity for the attractor of a partially dissipative model of Bénard convection in a  porous medium, Journal of Differential Equations,  163 (2000), 292-311.

 

56. S. Chen, C. Foias, D. Holm, E. Olson, E.S. Titi, and S. Wynne, The Camassa--Holm equations  and turbulence, Physica D, 133  (1999), 49-65.

 

55.  S. Shvartsman, C. Theodoropoulos, R. Rico-Martinez,  I.G. Kevrekidis, E.S. Titi, and T. J. Mountziares, Order reduction of nonlinear dynamic models for distributed   reacting systems, Journal of Process Control, 10 (2000), 177-184.

 

54. S. Chen, C. Foias, D. Holm, E. Olson, E.S. Titi and S. Wynne, A connection between Camass-Holm equations and turbulent flows in channels and pipes, Physics of Fluids,  11 (1999), 2343-2353.

 

53. S. Chen, C. Foias, D. Holm, E.  Olson, E.S. Titi  and S. Wynne, The Camassa--Holm equations as a closure model for turbulent channel flow, Physical Review Letters, 81 (1998), 5338-5341.

 

52. B. García-Archilla and E.S. Titi, Postprocessing the Galerkin method:  The finite elements case, SIAM, Journal of Numerical Analysis, 37 (2000), 470-499.

 

51. C. Cao, M. Rammaha and E.S. Titi, The Navier-Stokes equations on the rotating  2-D sphere: Gevrey regularity and asymptotic degrees of freedom, Zeitschrift für Angewandte Mathematik und Physik (ZAMP), 50 (1999), 341-360.

 

50.  H. Van Ly and E.S. Titi, Global Gevrey regularity for 3-D Bénard convection in porous medium with zero Darcy-Prandtl number, Journal of Nonlinear Science, 9 (1999), 333-362.

 

43. A. Ferrari and E.S. Titi, Gevrey regularity for nonlinear analytic parabolic equations, Communications in Partial Differential Equations, 23 (1998), 1-16.

 

26.  D. Jones and E.S. Titi, Upper bounds on the number of determining modes, nodes, and volume elements  for the Navier-Stokes equations, Indiana University Mathematics Journal, 42  (1993),  875-887. (A special issue in honor of Professor C. Foias on the occasion of his 60th Birthday).

 

25. J. Duan, P. Holmes and E.S. Titi, Regularity, approximation and asymptotic dynamics for a generalized Ginzburg-Landau equation, Nonlinearity, 6 (1993), 915-933.

 

24. G. Ponce, R. Racke, T.C. Sideris and E.S. Titi, Global  stability of large solutions to the 3-D Navier-Stokes equations,  Communications in Mathematical Physics, 159 (1993),  329-341.

 

23. A. Doelman and E.S. Titi, Regularity of solutions and the convergence of the Galerkin method in the Ginzburg-Landau equation, Numerical Functional Analysis and Optimization, 14 (1993), 299-321.

 

2. E.S. Titi, On a criterion for locating stable stationary solutions to the Navier-Stokes equations,  Nonlinear Analysis, Theory, Methods and Applications,   11 (1987), 1085-1102.