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The 2D Boussinesq-Navier-Stokes Equations with Logarithmically Supercritical Dissipation

The 2D Boussinesq-Navier-Stokes Equations with Logarithmically Supercritical Dissipation
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Year:    2024

Author:    Durga Jang K.C., Dipendra Regmi, Lizheng Tao, Jiahong Wu

Journal of Mathematical Study, Vol. 57 (2024), Iss. 1 : pp. 101–132

Abstract

We study the global well-posedness of the initial-value problem for the 2D Boussinesq-Navier-Stokes equations with dissipation given by an operator $\mathcal{L}$ that can be defined through both an integral kernel and a Fourier multiplier.  When the operator $\mathcal{L}$ is represented by $\frac{|\xi|}{a(|\xi|)}$ with $a$ satisfying $ \lim_{|\xi|\to \infty} \frac{a(|\xi|)}{|\xi|^\sigma} = 0$ for any $\sigma>0$, we obtain the global well-posedness.  A special consequence is the global well-posedness of 2D Boussinesq-Navier-Stokes equations when the dissipation is logarithmically supercritical.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jms.v57n1.24.06

Journal of Mathematical Study, Vol. 57 (2024), Iss. 1 : pp. 101–132

Published online:    2024-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    32

Keywords:    Supercritical Boussinesq-Navier-Stokes equations global regularity.

Author Details

Durga Jang K.C.

Dipendra Regmi

Lizheng Tao

Jiahong Wu