# On the Small Noise Limit For Some Non-Linear SPDEs with Vanishing Noise Correlation

### On the Small Noise Limit For Some Non-Linear SPDEs with Vanishing Noise Correlation

Series: Mathematics Colloquium
Location: Math 501
Presenter: Sandra Cerrai, University of Maryland

"We are dealing with the study of the validity of a large deviation principle for some nonlinear PDEs, perturbed by a Gaussian random forcing. We are here interested in the regime where both the strength of the noise and its correlation are vanishing, on a length scale $\epsilon$ and $\delta$, respectively, with $0<\epsilon,\delta<<1$. Depending on the relationship between $\epsilon$ and $\delta$ we will prove the validity of the large deviation principle in different functional spaces. We will illustrate our method by considering the two-dimensional stochastic Navier-Stokes equation and a class of stochastic reaction-diffusion equations, defined in any space dimension, including the dynamical $\Phi^{2n}_d$ model."

Refreshments in Math Commons Room at 3:30pm