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

Abstract

We investigate a micro-scale model of superfluidity derived by Pitaevskii in 1959 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 (NSE), 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 ${\mathbb{T}}^2$ -- strong in wavefunction and velocity, and weak in density.

arXiv comment34 pages. Minor errors corrected. arXiv admin note: text overlap with arXiv:2106.04659

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Cited by in corpus (1)

• On the mass transfer in the 3D Pitaevskii model