The existence and uniqueness of weak solutions for a highly nonlinear shallow-water model with Coriolis effect

IF 1.2 3区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Journal of Mathematical Physics Pub Date : 2024-08-19 DOI:10.1063/5.0201600

Shouming Zhou, Jie Xu

引用次数: 0

Abstract

In this paper, we consider the Cauchy problem for a highly nonlinear shallow water model arising from the full water waves with Coriolis effect. The existence of weak solutions to the equation in the lower order Sobolev space Hs(R) with 1<s≤32 is presented. Moreover, the local well-posedness of strong solutions in Sobolev space Hs(R) with s>32 is established by the pseudoparabolic regularization technique.

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具有科里奥利效应的高度非线性浅水模型弱解的存在性和唯一性

本文考虑了由具有科里奥利效应的全水波引起的高度非线性浅水模型的 Cauchy 问题。提出了方程在 1<s≤32 的低阶 Sobolev 空间 Hs(R) 中弱解的存在性。此外，还通过伪抛物正则化技术建立了 s>32 的 Sobolev 空间 Hs(R) 中强解的局部好求解性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Mathematical Physics 物理-物理：数学物理

CiteScore

2.20

自引率

15.40%

发文量

396

审稿时长

4.3 months

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