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

• URL: http://arxiv.org/abs/2305.12496v2
• Date: Mon, 29 Jan 2024 02:16:00 GMT
• Title: Small-data global existence of solutions for the Pitaevskii model of superfluidity
• Authors: Juhi Jang, Pranava Chaitanya Jayanti, Igor Kukavica
• Abstract summary: 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. We prove global/almost global existence of solutions to this system in $mathbbT2$ -- strong in wavefunction and velocity, and weak in density.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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 Schr\"odinger 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.

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