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arXiv · 2205.10331

On the regularity of temperature fronts for the 3D viscous Boussinesq system

Omar Lazar·Yatao Li·Liutang Xue
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Abstract

We study the temperature front problem for the 3D viscous Boussinesq equation. We prove that the $C^{k,\gamma}$ ($k\geq 1$, $0<\gamma< 1$) and $W^{2,\infty}$ regularity of a temperature front is locally preserved along the evolution as well as globally preserved under a smallness condition in a critical space. In particular, beside giving another proof of the main result in \cite{GGJ20}, we also extend it to a more general class of regular patch.

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Omar Lazar, Yatao Li, Liutang Xue. 2022-05-20. On the regularity of temperature fronts for the 3D viscous Boussinesq system. https://arxiv.org/abs/2205.10331

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