Global Regularity of the 2D HVBK equations

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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