@article{Silvestre2023, 
author = {Luis Silvestre and Stanley Snelson},
title = {Solutions to the non-cutoff Boltzmann equation uniformly near a Maxwellian},
year = {2023},
journal = {Mathematics in Engineering},
volume = {5},
number = {2},
pages = {1-36},
keywords = {Boltzmann equation, global existence, perturbation of equilibrium, conditional regularity, long-range interactions},
url = {https://www.sciopen.com/article/10.3934/mine.2023034},
doi = {10.3934/mine.2023034},
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∞ 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.}
}