Stochastically forced compressible Navier-Stokes equations with slip boundary conditions of friction type
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917217267875840 |
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| author | Tsuboya, Reo |
| author_facet | Tsuboya, Reo |
| contents | We study a mathematical model of a compressible viscous fluid driven by stochastic forces under slip boundary conditions of friction type. We introduce a notion of a weak solution that is analytically and probabilistically consistent with this model. Our main result establishes the existence of such weak solutions under slip boundary conditions on bounded domains with $C^{2+ν}$-boundary ($ν>0$). The proof of this result combines an extended version of the four-layer approximation scheme on the torus by Breit/Feireisl/Hofmanová (2018) with the convex approximation method for absolute value functions studied by Nečasová/Ogorzaly/Scherz (2023). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_15768 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Stochastically forced compressible Navier-Stokes equations with slip boundary conditions of friction type Tsuboya, Reo Probability Analysis of PDEs 60H15, 35Q30, 76N10, 76M35 We study a mathematical model of a compressible viscous fluid driven by stochastic forces under slip boundary conditions of friction type. We introduce a notion of a weak solution that is analytically and probabilistically consistent with this model. Our main result establishes the existence of such weak solutions under slip boundary conditions on bounded domains with $C^{2+ν}$-boundary ($ν>0$). The proof of this result combines an extended version of the four-layer approximation scheme on the torus by Breit/Feireisl/Hofmanová (2018) with the convex approximation method for absolute value functions studied by Nečasová/Ogorzaly/Scherz (2023). |
| title | Stochastically forced compressible Navier-Stokes equations with slip boundary conditions of friction type |
| topic | Probability Analysis of PDEs 60H15, 35Q30, 76N10, 76M35 |
| url | https://arxiv.org/abs/2601.15768 |