# Global existence of renormalized solutions to Boltzmann equations with incoming boundary condition and non-cutoff kernel

## TL;DR

This paper proves the global existence of renormalized solutions to the Boltzmann equation with non-cutoff kernels in bounded domains with incoming boundary conditions, extending previous results to more realistic physical settings.

## Contribution

It extends the existence theory of Boltzmann solutions to bounded domains with incoming boundary conditions for non-cutoff kernels, which was previously known mainly for whole spaces or periodic domains.

## Key findings

- Established global renormalized solutions in bounded domains
- Extended non-cutoff kernel results to bounded domains with boundary conditions
- Bridged gap between theory in whole space and bounded domain settings

## Abstract

We prove the existence of global renormalized solutions to the Boltzmann equation in bounded domain with incoming boundary condition, with non-cutoff collision kernels. Thus we extend the results of \cite{villani2002noncutoff} for whole spaces or periodic domain to bounded domains endorsed with incoming boundary condition.