Well-Posedness of the generalised Dean-Kawasaki Equation with correlated noise on bounded domains
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916432947707904 |
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| author | Popat, Shyam |
| author_facet | Popat, Shyam |
| contents | In this paper, we extend the notion of stochastic kinetic solutions introduced in arXiv:2108.08858 to establish the well-posedness of stochastic kinetic solutions of generalized Dean-Kawasaki equations with correlated noise on bounded, $C^2$-domains with Dirichlet boundary conditions. The results apply to a wide class of non-negative boundary data, which is based on certain a priori estimates for the solutions, that encompasses all non-negative constant functions including zero and all smooth functions bounded away from zero. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_19466 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Well-Posedness of the generalised Dean-Kawasaki Equation with correlated noise on bounded domains Popat, Shyam Probability Analysis of PDEs In this paper, we extend the notion of stochastic kinetic solutions introduced in arXiv:2108.08858 to establish the well-posedness of stochastic kinetic solutions of generalized Dean-Kawasaki equations with correlated noise on bounded, $C^2$-domains with Dirichlet boundary conditions. The results apply to a wide class of non-negative boundary data, which is based on certain a priori estimates for the solutions, that encompasses all non-negative constant functions including zero and all smooth functions bounded away from zero. |
| title | Well-Posedness of the generalised Dean-Kawasaki Equation with correlated noise on bounded domains |
| topic | Probability Analysis of PDEs |
| url | https://arxiv.org/abs/2403.19466 |