Landau-Lifshitz-Navier-Stokes Equations: Large Deviations and Relationship to The Energy Equality

• Authors: Benjamin Gess, Daniel Heydecker, Zhengyan Wu
• First public date: 2023-11-03
• arXiv: 2311.02223
• Preprint year: 2023
• Status: Accepted / forthcoming
• Publication type: Journal article
• Forthcoming in: Annals of Applied Probability
• Publication details: Author’s publication list

Abstract

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.

Associated SAiS members

• Benjamin Gess

Research areas

• Non-equilibrium Statistical Mechanics, Interacting Particle Systems and Fluctuating Hydrodynamics
• Stochastic Fluid Dynamics

BibTeX

@article{arxiv231102223,
  title = {Landau-Lifshitz-Navier-Stokes Equations: Large Deviations and Relationship to The Energy Equality},
  author = {Benjamin Gess and Daniel Heydecker and Zhengyan Wu},
  year = {2023},
  eprint = {2311.02223},
  archivePrefix = {arXiv},
  primaryClass = {math.PR}
}