Small-data global existence of solutions for the Pitaevskii model of superfluidity
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866916212312637440 |
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| author | Jang, Juhi Jayanti, Pranava Chaitanya Kukavica, Igor |
| author_facet | Jang, Juhi Jayanti, Pranava Chaitanya Kukavica, Igor |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2305_12496 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Small-data global existence of solutions for the Pitaevskii model of superfluidity Jang, Juhi Jayanti, Pranava Chaitanya Kukavica, Igor Analysis of PDEs Other Condensed Matter Fluid Dynamics Quantum Physics 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. |
| title | Small-data global existence of solutions for the Pitaevskii model of superfluidity |
| topic | Analysis of PDEs Other Condensed Matter Fluid Dynamics Quantum Physics |
| url | https://arxiv.org/abs/2305.12496 |