Analytical and Computational Challenges of Incompressible Flows at High Reynolds Number

CSIC Building (#406), Seminar Room 4122.
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The Nonlinear Schrödinger Equation as a Compressible Dispersive

Dr. Manoussos Grillakis

Mathematics at University of Maryland

Abstract:   Nonlinear Schrödinger equations arise in a variety of contexts, nonlinear optics, condensed matter and geometric evolution problems. Energy type estimates are a unifying theme for these equations and they offer the possibility of genuinely nonlinear apriori estimates. I will examine the conservation laws of these equations and explain how to obtain some old and new apriori estimates. The point of view is that one can obtain useful qualitative information by thinking of the Schrödinger equation as the evolution of a fluid.

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