Asymptotic Limits for Some Stochastic PDEs

Abstract:

In modern probability theory the large deviation principle gives an exponential bound on the probability of the norm of the solution getting above a threshold. We prove this theory by the use of weak convergence approach and classical Azencott method for 2D stochastic Navier-Stokes equations, 2D stochastic Boussinesq equation and 1D stochastic Schrodinger equation. As a consequence, we prove the law of the iterated logarithm and exit problem for Navier-Stokes and Schrodinger equations. These results are from joint work with Zhaoyang Qiu under the supervision of Prof. Dehua Wang.