On the Classical Solutions of Two Dimensional Inviscid Rotating Shallow Water System
Abstract
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. One of the key steps is a reformulation of the problem into a symmetric quasilinear Klein-Gordon system, for which the global existence of classical solutions is then proved 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.
Cite
@article{arxiv.0906.4797,
title = {On the Classical Solutions of Two Dimensional Inviscid Rotating Shallow Water System},
author = {Bin Cheng and Chunjing Xie},
journal= {arXiv preprint arXiv:0906.4797},
year = {2009}
}
Comments
1st version: 23 pages. 2nd version: add references at the end of second paragraph after Theorem 1.1; the third paragraph after Theorem 1.2 is newly added; definition of X(t) in (4.1) is slightly changed; proof of Lemma 4.2 is shortened