Solutions to the non-cutoff Boltzmann equation uniformly near a Maxwellian
Solutions to the non-cutoff Boltzmann equation uniformly near a Maxwellian
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DOI：
10.3934/mine.2023034
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发表时间：
2021-06
影响因子：
1
通讯作者：
L. Silvestre;Stanley Snelson
中科院分区：
文献类型：
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作者：
L. Silvestre;Stanley Snelson
本文的目的是结合已知的收敛于平衡点的结果和条件正则性，以及一个短时间的存在性结果，快速地证明了当初始数据接近平衡点时，非截断Boltzmann方程整体光滑解的存在性。我们给出了多项式加权的$L^\inty$初始数据的一个短时存在性结果。由此，我们推论，如果初始数据在这个范数下足够接近于麦克斯韦函数，则在时间上全局存在光滑解。
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.