Conditional regularity for the compressible Navier-Stokes equations with potential temperature transport
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| author | Lukáčová-Medviďová, Mária Schömer, Andreas |
| author_facet | Lukáčová-Medviďová, Mária Schömer, Andreas |
| contents | We study conditional regularity for the compressible Navier-Stokes equations with potential temperature transport in a bounded domain $Ω\subset\mathbb{R}^d$, $d\in\{2,3\}$, with no-slip boundary conditions. We first prove the existence and uniqueness of local-in-time strong solutions. Further, we prove a blow-up criterion for the strong solution in terms of $L^\infty$-norms for the density and the velocity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_14849 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Conditional regularity for the compressible Navier-Stokes equations with potential temperature transport Lukáčová-Medviďová, Mária Schömer, Andreas Analysis of PDEs We study conditional regularity for the compressible Navier-Stokes equations with potential temperature transport in a bounded domain $Ω\subset\mathbb{R}^d$, $d\in\{2,3\}$, with no-slip boundary conditions. We first prove the existence and uniqueness of local-in-time strong solutions. Further, we prove a blow-up criterion for the strong solution in terms of $L^\infty$-norms for the density and the velocity. |
| title | Conditional regularity for the compressible Navier-Stokes equations with potential temperature transport |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2407.14849 |