Fluctuating Hydrodynamics of the Ising-Kac-Kawasaki Model and Nonlinear Fluctuations Near Criticality
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908665406029824 |
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| author | Wu, Zhengyan |
| author_facet | Wu, Zhengyan |
| contents | We study the scaling limit behavior of a family of conservative SPDEs as the fluctuating Ising-Kac-Kawasaki dynamics. Precisely, we show that there exists a sequence of the one-dimensional rescaled fluctuating Ising-Kac-Kawasaki equation converges to the solution of the stochastic Cahn-Hilliard equation. This solves a simple version of the conjecture concerning the nonlinear fluctuation phenomenon, proposed by [Giacomin, Lebowitz, Presutti; Math. Surveys Monogr., 1999]. Furthermore, we prove a multi-scale dynamical large deviations in a small noise regime. Finally, we show the $Γ$-convergence of the rate function for the rescaled fluctuating Ising-Kac-Kawasaki equation to the rate function of the Cahn-Hilliard equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_15263 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fluctuating Hydrodynamics of the Ising-Kac-Kawasaki Model and Nonlinear Fluctuations Near Criticality Wu, Zhengyan Probability Analysis of PDEs We study the scaling limit behavior of a family of conservative SPDEs as the fluctuating Ising-Kac-Kawasaki dynamics. Precisely, we show that there exists a sequence of the one-dimensional rescaled fluctuating Ising-Kac-Kawasaki equation converges to the solution of the stochastic Cahn-Hilliard equation. This solves a simple version of the conjecture concerning the nonlinear fluctuation phenomenon, proposed by [Giacomin, Lebowitz, Presutti; Math. Surveys Monogr., 1999]. Furthermore, we prove a multi-scale dynamical large deviations in a small noise regime. Finally, we show the $Γ$-convergence of the rate function for the rescaled fluctuating Ising-Kac-Kawasaki equation to the rate function of the Cahn-Hilliard equation. |
| title | Fluctuating Hydrodynamics of the Ising-Kac-Kawasaki Model and Nonlinear Fluctuations Near Criticality |
| topic | Probability Analysis of PDEs |
| url | https://arxiv.org/abs/2511.15263 |