Dissipative Measure Valued Solutions to the Stochastic Compressible Navier-Stokes Equations and Inviscid-Incompressible Limit
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866911093965717504 |
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| author | Sarkar, Utsab |
| author_facet | Sarkar, Utsab |
| contents | We introduce a concept of dissipative measure valued martingale solutions for stochastic compressible Navier-Stokes equations. These solutions are weak from a probabilistic perspective, since they include both the driving Wiener process and the probability space as an integral part of the solution. Then, for the stochastic compressible Navier-Stokes system, we establish the relative energy inequality, and as a result, we demonstrate the path-wise weak-strong uniqueness principle. We also look at the inviscid-incompressible limit of the underlying system of equations using the relative energy inequality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_13140 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Dissipative Measure Valued Solutions to the Stochastic Compressible Navier-Stokes Equations and Inviscid-Incompressible Limit Sarkar, Utsab Probability Analysis of PDEs 35R60, 60H30, 60H15, 76M35 We introduce a concept of dissipative measure valued martingale solutions for stochastic compressible Navier-Stokes equations. These solutions are weak from a probabilistic perspective, since they include both the driving Wiener process and the probability space as an integral part of the solution. Then, for the stochastic compressible Navier-Stokes system, we establish the relative energy inequality, and as a result, we demonstrate the path-wise weak-strong uniqueness principle. We also look at the inviscid-incompressible limit of the underlying system of equations using the relative energy inequality. |
| title | Dissipative Measure Valued Solutions to the Stochastic Compressible Navier-Stokes Equations and Inviscid-Incompressible Limit |
| topic | Probability Analysis of PDEs 35R60, 60H30, 60H15, 76M35 |
| url | https://arxiv.org/abs/2212.13140 |