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

TL;DR

This paper proves the local-in-time existence of unique analytic solutions for a 3D inviscid superfluidity model coupling Euler equations with a nonlinear mutual friction term.

Contribution

First rigorous construction of local-in-time analytic solutions for the inviscid 3D HVBK superfluidity system.

Findings

Existence of unique local-in-time solutions established.

Solutions are analytic in both time and space.

This work advances mathematical understanding of superfluid models.

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.