Regularity results for viscous 3D Boussinesq temperature fronts

TL;DR

This paper studies the evolution and regularity of temperature fronts in the 3D viscous Boussinesq system, establishing local existence and global regularity propagation for small initial data, even with complex front structures.

Contribution

It introduces new techniques to handle general temperature fronts with piecewise Hölder regularity, extending previous results to more complex interface geometries.

Findings

Local in time existence for arbitrary initial data size.

Global regularity propagation for small initial data.

Handles general fronts with piecewise Hölder temperature profiles.

Abstract

This paper is about the dynamics of non-diffusive temperature fronts evolving by the incompressible viscous Boussinesq system in $\mathbb{R}^3$. We provide local in time existence results for initial data of arbitrary size. Furthermore, we show global in time propagation of regularity for small initial data in critical spaces. The developed techniques allow to consider general fronts where the temperature is piecewise H\"older (not necessarily constant), which preserve their structure together with the regularity of the evolving interface.