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arXiv · 2001.09119

Global Regularity of the 2D HVBK equations

Pranava Chaitanya Jayanti·Konstantina Trivisa
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Abstract

The Hall-Vinen-Bekharevich-Khalatnikov (HVBK) equations are a macroscopic model of superfluidity at non-zero temperatures. For smooth, compactly supported data, we prove the global well-posedness of strong solutions to these equations in $\mathbb{R}^2$, in the incompressible and isothermal case. The proof utilises a contraction mapping argument to establish local well-posedness for high-regularity data, following which we demonstrate global regularity using an analogue of the Beale-Kato-Majda criterion in this context. In the appendix, we address the sufficient conditions on a 2D vorticity field, in order to have a finite kinetic energy.

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Pranava Chaitanya Jayanti, Konstantina Trivisa. 2020-03-24. Global Regularity of the 2D HVBK equations. https://doi.org/10.1007/s00332-020-09666-1

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