Donsker-Varadhan large deviation principle for locally damped and randomly forced NLS equations

Abstract

We study large deviations from the invariant measure for nonlinear Schrödinger equations with colored noises on determining modes. The proof is based on a new abstract criterion, inspired by [V. Jakšić et al., Comm. Pure Appl. Math., 68 (2015), 2108-2143]. To address the difficulty caused by fixed squeezing rate, we introduce a bootstrap argument to derive Lipschitz estimates for Feynman-Kac semigroups. This criterion is also applicable to wave equations and Navier-Stokes system.