### Regularity estimates for the Boltzmann equation

*Luis Silvestre, University of Chicago*

The Boltzmann equation describes the evolution of particle densities, in terms of space and velocity, for gases and plasma. We will discuss the regularization effect of this equation in the inhomogeneous, non-cutoff case. We prove that the solution remains bounded and Holder continuous for as long as its associated hydrodynamic quantities are bounded and away from vacuum. Our analysis is based on techniques that originate in the study of parabolic integro-differential equations.