##### Department of Mathematics,

University of California San Diego

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### Math 248- Analysis Seminar

## Stanley Snelson

#### Florida Institute of Technology

## Coercive lower bounds and vacuum-filling in the Boltzmann equation

##### Abstract:

In this talk, we describe self-generating pointwise lower bounds for solutions of the non-cutoff Boltzmann equation, which models the evolution of the particle density of a diffuse gas. These lower bounds imply that vacuum regions in the initial data are filled instantaneously, and also lead to key coercivity estimates for the collision operator. As an application, we can remove the assumptions of mass bounded below and entropy bounded above, from the known criteria for smoothness and continuation of solutions. The proof strategy also applies to the Landau equation, and we will compare this (deterministic) proof with our prior (probabilistic) proof of lower bounds for the Landau equation. This talk is based on joint work with Chris Henderson and Andrei Tarfulea.

Host: Tarek Elgindi

### March 10, 2020

### 11:00 AM

### AP&M 7321

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