The dynamic phi^4 model comes down from infinity

Jean-Christophe Mourrat
ENS Lyon
Friday, November 10, 2017 -
2:30pm to 3:30pm
Vincent Hall 206

The dynamic phi^4 model is a parabolic stochastic PDE with a cubic non-linearity and an additive white-noise forcing. We will focus on the case where the space variable ranges in the 3-dimensional torus. Due to the roughness of the noise, the equation needs to be renormalised in order to make sense. I will review this and discuss the proof that the solution "comes down from infinity": measured in the right norm, the solution decays essentially like (1+t)^{-1/2}, uniformly over the initial condition. This is joint work with Hendrik Weber.