A new stability result for the 2D Boussinesq equations with horizontal dissipation

For \(\mathbb{R}^2\), the stability of smooth solutions of 2D anisotropic Boussinesq equations with horizontal dissipation is an open problem. In this work, we present a partial answer to this problem in a rougher function space \(H^{0,s}(\mathbb{R}^2)\). Moreover, the previous stability results wit...

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Bibliographic Details
Published inarXiv.org
Main Authors Hong Sung Jin, Kwak, Minkyu, Lkhagvasuren, Bataa
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 26.01.2024
Subjects
Boussinesq equations
Dissipation
Function space
Mathematical analysis
Stability
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Summary:For \(\mathbb{R}^2\), the stability of smooth solutions of 2D anisotropic Boussinesq equations with horizontal dissipation is an open problem. In this work, we present a partial answer to this problem in a rougher function space \(H^{0,s}(\mathbb{R}^2)\). Moreover, the previous stability results with the regularity index \(\frac 12<s<1\) is extended to an integer \(1\le s\) and the elementary techniques are used.
ISSN:2331-8422