Probability and Mathematical Physics Seminar

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The Gaussian Structure of the Stochastically Forced Burgers Equation below KPZ

Speaker: Jonathan Mattingly, Duke University

Location: Warren Weaver Hall 1302

Date: Friday, December 13, 2024, 11:10 a.m.

Synopsis:

I will explain some recent results which show that the law of the stochastic burgers equation at a fixed time t is absolutely continuous with respect to the natural Gaussian measure on the spatial domain. The results will apply to forcing just up to the point where the roughness of the forcing corresponds to the classical KPZ equation in the Burgers setting. As one approaches  this level of roughness, the equations must be understood as a Singular SPDEs (in the sense of Hairer ).  As such the construction helps illuminate the structure of the equation and makes clear in what sense we might call these equations “truly” elliptic in this infinite dimensional setting. I will also make comments connecting back to previous results on the 2D Naiver Stokes equation. This work is joint with Marco Romito and Langxuan Su and builds on work with Andrea Watkins Hairston.