On the mass transfer in the 3D Pitaevskii model
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917666128658432 |
|---|---|
| author | Jang, Juhi Jayanti, Pranava Chaitanya Kukavica, Igor |
| author_facet | Jang, Juhi Jayanti, Pranava Chaitanya Kukavica, Igor |
| contents | 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 Schrödinger 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_06305 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the mass transfer in the 3D Pitaevskii model Jang, Juhi Jayanti, Pranava Chaitanya Kukavica, Igor Analysis of PDEs Fluid Dynamics Quantum Physics 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 Schrödinger 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. |
| title | On the mass transfer in the 3D Pitaevskii model |
| topic | Analysis of PDEs Fluid Dynamics Quantum Physics |
| url | https://arxiv.org/abs/2310.06305 |