Stationary solution to Stochastically Forced Euler-Poisson Equations in Bounded Domain: Part 1. 3-D Insulating Boundary
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866913691888254976 |
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| author | Li, Yachun Mei, Ming Zhang, Lizhen |
| author_facet | Li, Yachun Mei, Ming Zhang, Lizhen |
| contents | This paper is concerned with $3$-D stochastic Euler-Poisson equations with insulating boundary conditions forced by the Wiener process. We first establish the global existence and uniqueness of the solution to the system, then we prove that the solution converges to its steady-state time-asymptotically. To obtain the converging rate, we need to develop weighted energy estimates, which are not required for the deterministic counterpart of the problem. Moreover, we observe that the invariant measure is just the Dirac measure generated by the steady-state, in which the time-exponential convergence rate to the steady-state plays an essential role. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_00017 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stationary solution to Stochastically Forced Euler-Poisson Equations in Bounded Domain: Part 1. 3-D Insulating Boundary Li, Yachun Mei, Ming Zhang, Lizhen Analysis of PDEs Probability 34D05, 34D20, 35B35, 35K51, 60H15, 82D37 This paper is concerned with $3$-D stochastic Euler-Poisson equations with insulating boundary conditions forced by the Wiener process. We first establish the global existence and uniqueness of the solution to the system, then we prove that the solution converges to its steady-state time-asymptotically. To obtain the converging rate, we need to develop weighted energy estimates, which are not required for the deterministic counterpart of the problem. Moreover, we observe that the invariant measure is just the Dirac measure generated by the steady-state, in which the time-exponential convergence rate to the steady-state plays an essential role. |
| title | Stationary solution to Stochastically Forced Euler-Poisson Equations in Bounded Domain: Part 1. 3-D Insulating Boundary |
| topic | Analysis of PDEs Probability 34D05, 34D20, 35B35, 35K51, 60H15, 82D37 |
| url | https://arxiv.org/abs/2408.00017 |