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arXiv · 2310.06305

On the mass transfer in the 3D Pitaevskii model

Juhi Jang·Pranava Chaitanya Jayanti·Igor Kukavica
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Abstract

We examine a micro-scale model of superfluidity derived by Pitaevskii in 1959 which describes the interacting dynamics between superfluid He-4 and its normal fluid phase. This system consists of the nonlinear Schr\"odinger equation and the incompressible, inhomogeneous Navier-Stokes equations, coupled to each other via a bidirectional nonlinear relaxation mechanism. The coupling permits mass/momentum/energy transfer between the phases, and accounts for the conversion of superfluid into normal fluid. We prove the existence of weak solutions in $\mathbb{T}^3$ for a power-type nonlinearity, beginning from small initial data. The main challenge is to control the inter-phase mass transfer in order to ensure the strict positivity of the normal fluid density, while obtaining time-independent a priori estimates.

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Juhi Jang, Pranava Chaitanya Jayanti, Igor Kukavica. 2023-10-10. On the mass transfer in the 3D Pitaevskii model. https://doi.org/10.1007/s00021-024-00877-0

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