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Department of Mathematics |
Professor Edriss S. Titi
Mathematics, Mechanical and Aerospace Engineering
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Room 510C OFFICE HOURS:
Mondays and Wednesdays 12:00noon-1:00pm |
TEACHING
Math 2A
PUBLICATIONS
RECENT PREPRINTS
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, (submitted). (pdf)
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, (submitted).(pdf)
V.K. Kalantarov and E.S. Titi, Global
attractors and determining modes for the 3D Navier-Stokes-Voight equations,
(submitted). (pdf)
C. Cao, S. Chen and E.S. Titi, A turbulence model for the 1D dispersive wave,
(submitted). (pdf)
(
ps )
PAPERS TO APPEAR
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, (to appear).
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
) ( ps
)
SELECTED RECENTLY PUBLISHED JOURNAL PAPERS
114. C. Cao and E.S. Titi, Regularity
criteria for the three-dimensional
Navier-Stokes equations, Indiana University Mathematics Journal, (2008),(An
invite article for a special issue in honor of Professor C. Foias in the
occasion of his 75th birthday), (in press).
113. E. Olson and E.S. Titi, Determining modes and Grashof
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. (pdf)
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).
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. (pdf-English) (pdf-Russian).
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. (pdf)
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. (pdf)
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. (pdf)
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. (pdf)
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. (pdf)
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. (pdf)
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.(pdf)
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. (pdf)
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. (pdf)
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. (pdf)
90. A.A. Ilyin and E.S. Titi, The
damped-driven 2D Navier-Stokes system on large elongated domains, Journal
of Mathematical Fluid Mechanics, DOI10.1007/s00021-006-0226-6, (2007).
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. (pdf)
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. (pdf) (ps)
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. (pdf )(ps )
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.( pdf)( ps )
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. ( pdf ) ( ps )
77. C. Cao, E.S. Titi and M. Ziane, A
``horizontal" hyper--diffusion 3-D thermocline planetary geostrophic
model: well-posedness and long time behavior , Nonlinearity, 17 (2004), 1749-1776. (
pdf )(
ps ).
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. (English-
pdf
)(English-ps
)(Russian-pdf
)(Russian-ps
)
75. P. Constantin,
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, (pdf) (ps).
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. (
pdf ) (
ps)
72. H. Bellout,
71. P. Constantin, I. Kevrekidis and E.S. Titi, Remarks on a Smoluchowski equation, Discrete and Continuous Dynamical Systems, 11 (2004), 101-112. ( pdf) ( ps )
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. (pdf) ( ps )
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.( pdf ) ( ps )
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. (pdf ) ( ps )
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. ( pdf ) ( ps )
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. ( pdf ) (ps ).
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, (Special Issue in Honor of C. Foias and R. Temam), 50 (2001), 37-96. (pdf ) (ps )
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. ( pdf ) ( ps )
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, (Special Issue in Honor of V. E. Zakharov on the Occasion of His 60th Birthday), D152 (2001), 505-519. ( pdf )(ps )
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. Garcia--Archilla, J. Novo and E.S. Titi, Postprocessing
Fourier spectral methods: the case of smooth solutions, Applied
Numerical Mathematics, 43 (2002), 191-209. (pdf) (ps )
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. ( pdf ) ( ps )
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, D133 (1999), 49-65. ( pdf )(ps ).
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.( pdf )(ps )
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. ( pdf ) ( ps )
52. B. Garcia-Archilla and E.S. Titi, Postprocessing
the Galerkin method: The finite elements case,
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 fu"r 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. (pdf) (ps)
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. (Special Issue in Honor of
Professor C. Foias on the Occasion of his 60th Birthday). (pdf)
(ps)
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. (pdf)