Kinetic Description of Multiscale Phenomena

The Annual Kinetic FRG Meeting
September 21-25, 2009

CSIC Building (#406), Seminar Room 4122.

On the classical solutions of two dimensional inviscid rotating shallow water system

Dr. Bin Cheng

University of Michigan

Abstract:  Joint work with with Chunjing Xie. We prove global existence and asymptotic behavior of classical solutions for two dimensional inviscid Rotating Shallow Water system with small initial data subject to the zero-relative-vorticity constraint. Such global existence is in contrast with the finite time breakdown of compressible Euler equations in two and three dimensions. A key step in our proof is reformulation of the problem into a symmetric quasilinear Klein-Gordon system, which is then studied with combination of the vector field approach and the normal forms. We also probe the case of general initial data and reveal a lower bound for the lifespan that is almost inversely proportional to the size of the initial relative vorticity.