Conference Agenda

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 [QY98], with Landau-Lifschitz fluctuating hydrodynamics [LL87]. Secondly, 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.

Joint work with Daniel Heydecker and Zhengyan Wu.

We consider a singular stochastic reaction-diffusion equation with a cubic non-linearity on the 3D torus and study its behaviour as it exits a domain of attraction of an asymptotically stable point. Mirroring the results of Freidlin and Wentzell in the finite-dimensional case, we relate the logarithmic asymptotics of its mean exit time and exit place to the minima of the corresponding (quasi-)potential on the boundary of the domain. The challenge, in our setting, is that the stochastic equation is singular such that its solution only lives in a Hölder–Besov space of distributions. The proof accordingly combines a classical strategy with novel controllability statements as well as continuity and locally uniform large deviation results obtained via the theory of regularity structures.