Smoothing effect of weak solutions for the spatially homogeneous Boltzmann Equation without angular cutoff

Q2 Mathematics

Journal of Mathematics of Kyoto University Pub Date : 2011-04-29 DOI:10.1215/21562261-1625154

Radjesvarane Alexandre, Y. Morimoto, S. Ukai, Chao-Jiang Xu, Tong Yang

引用次数: 49

Abstract

In this paper, we consider the spatially homogeneous Boltzmann equation without angular cutoff. We prove that every $L^1$ weak solution to the Cauchy problem with finite moments of all order acquires the $C^\infty$ regularity in the velocity variable for the positive time.

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无角截断空间齐次玻尔兹曼方程弱解的平滑效应

本文考虑无角截断的空间齐次玻尔兹曼方程。证明了所有阶有限矩Cauchy问题的$L^1$弱解在正时间下速度变量具有$C^\infty$正则性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Mathematics of Kyoto University 数学-数学

CiteScore

1.20

自引率

0.00%

发文量

期刊介绍： Papers on pure and applied mathematics intended for publication in the Kyoto Journal of Mathematics should be written in English, French, or German. Submission of a paper acknowledges that the paper is original and is not submitted elsewhere.