Regularity Results for Viscous 3D Boussinesq Temperature Fronts

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 Hölder (not necessarily constant), which preserve their structure together with the regularity of the evolving interface.

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Acknowledgements

This research was partially supported by the Grant MTM2014-59488-P (Spain) and by the ERC through the Starting Grant project H2020-EU.1.1.-639227. EGJ was supported by MECD FPU Grant from the Spanish Government.

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Correspondence to Francisco Gancedo.

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Gancedo, F., García-Juárez, E. Regularity Results for Viscous 3D Boussinesq Temperature Fronts. Commun. Math. Phys. 376, 1705–1736 (2020). https://doi.org/10.1007/s00220-020-03767-4

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