# Analysis Seminar

#### Renormalized Martingale Solutions to the Boltzmann Equation with Stochastic Forcing

**Speaker:**
Sam Punshon-Smith, University of Maryland

**Location:**
Warren Weaver Hall 1302

**Date:**
Thursday, February 16, 2017, 11 a.m.

**Synopsis:**

The Boltzmann equation is often used to describe the non-equilibrium behavior of a collisional gas in a low density regime. Frequently an external forcing term is included to account for the influence of an external field interacting with the gas. In this talk we will study the Boltzmann equation in the presence of a white in time stochastic forcing. Such a forcing can be thought of as a kinetic analogue of stochastic forcing commonly included in fluid mechanical models of turbulence. Under certain spatial coloring assumptions on the noise, we obtain existence of global in time, probabilistically weak, renormalized (in the sense of DiPerna/Lions) solutions to this equation for a general class of \(L^1\) initial data. Among the topics discussed will be the renormalization theory of stochastic transport equations, velocity averaging of stochastic kinetic equations and various stochastic fluid limits.