This paper is about the dynamics of non-diffusive temperature fronts evolving by the incompressible viscous Boussinesq system in $${\mathbb {R}}^3$$ 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 Hölder (not necessarily constant), which preserve their structure together with the regularity of the evolving interface.

中文翻译：

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粘性 3D Boussinesq 温度前沿的规律性结果

本文是关于$${\mathbb {R}}^3$$ R 3 中不可压缩粘性Boussinesq系统演化的非扩散温度前沿的动力学。我们为任意大小的初始数据提供本地时间存在结果。此外，我们展示了关键空间中小初始数据的规律性的全局时间传播。开发的技术允许考虑温度为分段 Hölder（不一定恒定）的一般前沿，这些前沿保留了它们的结构以及不断变化的界面的规律性。