Local-in-time analytic solutions for an inviscid model of superfluidity in 3D

Abstract

We address the existence of solutions for the inviscid version of the Hall-Vinen-Bekharevich-Khalatnikov equations in 3D, a macro-scale model of superfluidity. This system couples the incompressible Euler equations for the normal fluid and superfluid using a nonlinear mutual friction term that acts only at points of non-zero superfluid vorticity. In the first rigorous study of the inviscid HVBK system, we construct a unique local-in-time solution that is analytic in time and space.