二维无粘旋转浅水系统的经典解
偏微分方程分析
2009-07-01 v2 数学物理
math.MP
摘要
我们证明了在零相对涡度约束下，具有小初始数据的二维无粘旋转浅水系统经典解的整体存在性和渐近行为。关键步骤之一是将问题重新表述为一个对称拟线性Klein-Gordon系统，然后结合向量场方法和正规形证明了该系统经典解的整体存在性。我们还探讨了一般初始数据的情况，并揭示了寿命的下界，该下界几乎与初始相对涡度的大小成反比。
引用
@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}
}
备注
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