Analysis Seminar

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The dynamic $\phi^4$ model comes down from infinity

Speaker: Jean-Christophe Mourrat, ENS Lyon

Location: Warren Weaver Hall 1302

Date: Thursday, December 7, 2017, 11 a.m.

Synopsis:

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.