On the mass transfer in the 3D Pitaevskii model
- URL: http://arxiv.org/abs/2310.06305v2
- Date: Thu, 11 Apr 2024 21:43:07 GMT
- Title: On the mass transfer in the 3D Pitaevskii model
- Authors: Juhi Jang, Pranava Chaitanya Jayanti, Igor Kukavica,
- Abstract summary: We examine a micro-scale model of superfluidity derived by Pitaevskii in 1959.
The system consists of the nonlinear Schr"odinger equation and the incompressible, inhomogeneous Navier-Stokes equations.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- 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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