Global Well-posedness of Some Equations for Atmospheric and Oceanic Dynamics

Speaker: 

Chongsheng Cao

Institution: 

Florida International University

Time: 

Friday, September 30, 2005 - 4:00pm

Location: 

MSTB 254

The primitive equations describe hydrodynamical flows in thin layers of fluid (such as the atmosphere and the oceans). Due to the shallowness of the fluid layer the
the vertical motion is much smaller than the horizontal one and hence the former is modeled, in the primitive equations, by the hydrostatic balance. The primitive equations are considered to be a very good model
for large scale ocean circulations and for global atmospheric flows. As a result they are used in most global climate models. In this talk we will introduce a mathematical framework for studying various models of atmospheric and oceanic dynamics. In particular, the planetary geostrophic equations and the primitive equations. Furthermore, I will show the global well posedness of these equations.

On Unique Continuation of Solutions of Schroedinger Equations

Speaker: 

Gustavo Ponce

Institution: 

University of California, Santa Barbara

Time: 

Friday, October 21, 2005 - 4:00pm

Location: 

MSTB 254

We study unique continuation properties of solutions of
linear and non-linear Schroedinger equations. In the nonlinear case we are interested in deducing uniqueness of the solution from information on the difference of two possible solutions at two different times.

Optimal Regularity and Nonlinear Parabolic Problems.

Speaker: 

Patrick Guidotti

Institution: 

University of California - Irvine

Time: 

Friday, October 7, 2005 - 4:00pm

Location: 

MSTB 254

This talk will give an introduction to optimal regularity as a tool to analyze (fully) nonlinear parabolic equations/systems. After a review of the major developments of the theory, the focus will shift to singular parabolic equations. It will be shown that optimal regularity results can be obtained for a large class of singular abstract Cauchy problems and, if time permits, applications of the theory will be presented.

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