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arXiv · 2306.10670

Global well-posedness for the 2D Euler-Boussinesq-B$\rm\acute{e}$nard equations with critical dissipation

Zhuan Ye
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Abstract

This present paper is dedicated to the study of the Cauchy problem of the two-dimensional Euler-Boussinesq-B$\rm\acute{e}$nard equations which couple the incompressible Euler equations for the velocity and a transport equation with critical dissipation for the temperature. We show that there is a global unique solution to this model with Yudovich's type data. This settles the global regularity problem which was remarked by Wu and Xue (J. Differential Equations 253:100--125, 2012).

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Zhuan Ye. 2023-06-19. Global well-posedness for the 2D Euler-Boussinesq-B$\rm\acute{e}$nard equations with critical dissipation. https://arxiv.org/abs/2306.10670

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