  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.
