Landau-Lifshitz-Navier-Stokes Equations: Large Deviations and Relationship to The Energy Equality
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| Format: | Preprint |
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2023
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| _version_ | 1866914704243294208 |
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| author | Gess, Benjamin Heydecker, Daniel Wu, Zhengyan |
| author_facet | Gess, Benjamin Heydecker, Daniel Wu, Zhengyan |
| contents | The dynamical large deviations principle for the three-dimensional incompressible Landau-Lifschitz-Navier-Stokes equations is shown, in the joint scaling regime of vanishing noise intensity and correlation length. This proves the consistency of the large deviations in lattice gas models \cite{QY}, with Landau-Lifschitz fluctuating hydrodynamics \cite{LL87}. Secondly, in the course of the proof, we unveil a novel relation between the validity of the deterministic energy equality for the deterministic forced Navier-Stokes equations and matching large deviations upper and lower bounds. In particular, we conclude that time-reversible uniqueness to the forced Navier-Stokes equations implies the validity of the energy equality, thus generalising the classical Lions-Ladyzhenskaya result. Thirdly, we prove that no non-trivial large deviations result can be true for local-in-time strong solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_02223 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Landau-Lifshitz-Navier-Stokes Equations: Large Deviations and Relationship to The Energy Equality Gess, Benjamin Heydecker, Daniel Wu, Zhengyan Probability The dynamical large deviations principle for the three-dimensional incompressible Landau-Lifschitz-Navier-Stokes equations is shown, in the joint scaling regime of vanishing noise intensity and correlation length. This proves the consistency of the large deviations in lattice gas models \cite{QY}, with Landau-Lifschitz fluctuating hydrodynamics \cite{LL87}. Secondly, in the course of the proof, we unveil a novel relation between the validity of the deterministic energy equality for the deterministic forced Navier-Stokes equations and matching large deviations upper and lower bounds. In particular, we conclude that time-reversible uniqueness to the forced Navier-Stokes equations implies the validity of the energy equality, thus generalising the classical Lions-Ladyzhenskaya result. Thirdly, we prove that no non-trivial large deviations result can be true for local-in-time strong solutions. |
| title | Landau-Lifshitz-Navier-Stokes Equations: Large Deviations and Relationship to The Energy Equality |
| topic | Probability |
| url | https://arxiv.org/abs/2311.02223 |