期刊
EMS SURVEYS IN MATHEMATICAL SCIENCES
卷 7, 期 1, 页码 117-172出版社
EUROPEAN MATHEMATICAL SOC
DOI: 10.4171/EMSS/37
关键词
Boltzmann equation; non-cut off assumption; regularity estimates
类别
资金
- NSF [DMS-1764285]
The Boltzmann equation is a nonlinear partial differential equation that plays a central role in statistical mechanics. From the mathematical point of view, the existence of global smooth solutions for arbitrary initial data is an outstanding open problem. In the present article, we review a program focused on the type of particle interactions known as non-cutoff. It is dedicated to the derivation of a priori estimates in C-infinity, depending only on physically meaningful conditions. We prove that the solution will stay uniformly smooth provided that its mass, energy and entropy densities remain bounded, and away from vacuum.
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