Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2022
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2207.12774 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866929322141417472 |
|---|---|
| author | Wang, Likun Wu, Zhengyan Zhang, Rangrang |
| author_facet | Wang, Likun Wu, Zhengyan Zhang, Rangrang |
| contents | Inspired by [Fehrman, Gess; Invent. Math., 2023] and [Fehrman, Gess; Arch. Ration. Mech. Anal., 2024], we consider the Dean-Kawasaki equation with singular interactions and correlated noise which can be viewed as fluctuating mean-field limits. By imposing the Ladyzhenskaya-Prodi-Serrin condition on the interaction kernel, the existence of probabilistic weak renormalized kinetic solutions is established. Further, under an additional integrability assumption on the divergence of the interaction kernel, a kinetic formulation approach is applied to derive pathwise uniqueness, leading to the strong well-posedness of the equation. As an application, we obtain the well-posedness of a conservative stochastic partial differential equations known as fluctuating Ising-Kac-Kawasaki dynamics, which paves a step on the conjecture concerning nonlinear fluctuations of Kawasaki dynamics proposed by [Giacomin, Lebowitz, Presutti; Math. Surveys Monogr., 1999]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_12774 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Dean-Kawasaki Equation with Singular Interactions and Applications to Dynamical Ising-Kac Model Wang, Likun Wu, Zhengyan Zhang, Rangrang Probability Inspired by [Fehrman, Gess; Invent. Math., 2023] and [Fehrman, Gess; Arch. Ration. Mech. Anal., 2024], we consider the Dean-Kawasaki equation with singular interactions and correlated noise which can be viewed as fluctuating mean-field limits. By imposing the Ladyzhenskaya-Prodi-Serrin condition on the interaction kernel, the existence of probabilistic weak renormalized kinetic solutions is established. Further, under an additional integrability assumption on the divergence of the interaction kernel, a kinetic formulation approach is applied to derive pathwise uniqueness, leading to the strong well-posedness of the equation. As an application, we obtain the well-posedness of a conservative stochastic partial differential equations known as fluctuating Ising-Kac-Kawasaki dynamics, which paves a step on the conjecture concerning nonlinear fluctuations of Kawasaki dynamics proposed by [Giacomin, Lebowitz, Presutti; Math. Surveys Monogr., 1999]. |
| title | Dean-Kawasaki Equation with Singular Interactions and Applications to Dynamical Ising-Kac Model |
| topic | Probability |
| url | https://arxiv.org/abs/2207.12774 |