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

Abstract

We study the temperature front problem for the 3D viscous Boussinesq equation. We prove that the $C^{k,\gamma }$ ($k\ge 1$, $0<\gamma <1$) 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.

38 pages

Cited by in corpus (1)

• A new approach for the regularity of weak solutions of the 3D Boussinesq system