From Stochastic Hamiltonian Systems to Stochastic Compressible Euler Equation
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866910876147122176 |
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| author | Correa, Jesus Olivera, Christian |
| author_facet | Correa, Jesus Olivera, Christian |
| contents | We study a stochastic Hamiltonian system of $N$ particles with many particles interacting through a potential whose range is large in comparison with the typical distance between neighbouring particles. It is shown that the empirical measures associated to the position and velocity of the system converge to the solutions of stochastic compressible Euler equations in the limit as the particle number tends to infinity. Moreover, we quantify the distance between particles and the limit in suitable Sobolev norm. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_08101 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | From Stochastic Hamiltonian Systems to Stochastic Compressible Euler Equation Correa, Jesus Olivera, Christian Analysis of PDEs Probability We study a stochastic Hamiltonian system of $N$ particles with many particles interacting through a potential whose range is large in comparison with the typical distance between neighbouring particles. It is shown that the empirical measures associated to the position and velocity of the system converge to the solutions of stochastic compressible Euler equations in the limit as the particle number tends to infinity. Moreover, we quantify the distance between particles and the limit in suitable Sobolev norm. |
| title | From Stochastic Hamiltonian Systems to Stochastic Compressible Euler Equation |
| topic | Analysis of PDEs Probability |
| url | https://arxiv.org/abs/2301.08101 |