Solutions to the non-cutoff Boltzmann equation uniformly near a Maxwellian

Luis Silvestre; Stanley Snelson

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arXiv · 2106.03909

Solutions to the non-cutoff Boltzmann equation uniformly near a Maxwellian

Luis Silvestre·Stanley Snelson

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Abstract

The purpose of this paper is to show how the combination of the well-known results for convergence to equilibrium and conditional regularity, in addition to a short-time existence result, lead to a quick proof of the existence of global smooth solutions for the non cutoff Boltzmann equation when the initial data is close to equilibrium. We include a short-time existence result for polynomially-weighted $L^\infty$ initial data. From this, we deduce that if the initial data is sufficiently close to a Maxwellian in this norm, then a smooth solution exists globally in time.

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Luis Silvestre, Stanley Snelson. 2021-06-07. Solutions to the non-cutoff Boltzmann equation uniformly near a Maxwellian. https://arxiv.org/abs/2106.03909

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