Small-data global existence of solutions for the Pitaevskii model of superfluidity

Abstract

We investigate a micro-scale model of superfluidity derived by Pitaevskii (1959 Sov. Phys. JETP 8 282–7) to describe the interacting dynamics between the superfluid and normal fluid phases of Helium-4. The model involves the nonlinear Schrödinger equation (NLS) and the Navier–Stokes equations, coupled to each other via a bidirectional nonlinear relaxation mechanism. Depending on the nature of the nonlinearity in the NLS, we prove global/almost global existence of solutions to this system in T2 —strong in wavefunction and velocity, and weak in density.