Zero-viscosity limit for Boussinesq equations with vertical viscosity and Navier boundary in the half plane

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-06-11 DOI:10.1016/j.nonrwa.2024.104150

Mengni Li , Yan-Lin Wang

引用次数: 0

Abstract

In this paper we study the zero-viscosity limit of 2-D Boussinesq equations with vertical viscosity and zero diffusivity, which is a nonlinear system with partial dissipation arising in atmospheric sciences and oceanic circulation. The domain is taken as $R_{+}^{2}$ with Navier-type boundary. We prove the nonlinear stability of the approximate solution constructed by boundary layer expansion in conormal Sobolev space. The expansion order and convergence rates for the inviscid limit are also identified in this paper. Our paper extends a partial zero-dissipation limit result of Boussinesq system with full dissipation by Chae D. (2006) in the whole space to the case with partial dissipation and Navier boundary in the half plane.

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半平面上具有垂直粘性和纳维边界的布森斯克方程的零粘性极限

本文研究了具有垂直粘性和零扩散性的二维布森斯克方程的零粘性极限，这是一个在大气科学和海洋环流中出现的具有部分耗散的非线性系统。域取 R+2，边界为 Navier 型。我们证明了通过边界层扩展在常模 Sobolev 空间构建的近似解的非线性稳定性。本文还确定了不粘性极限的扩展阶数和收敛速率。本文将 Chae D. (2006) 提出的全耗散 Boussinesq 系统的部分零耗散极限结果在整个空间的应用扩展到了部分耗散和半平面 Navier 边界的情况。

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.