On measure solutions of the Boltzmann equation, part I: Moment production and stability estimates

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:252

Article

Lu, Xuguang²  Mouhot, Clement¹ 

[1] Univ Cambridge, Ctr Math Sci, DPMMS, Cambridge CB3 0WA, England

[2] Tsinghua Univ, Dept Math Sci, Beijing 100084, Peoples R China

关键词: Boltzmann equation;    Spatially homogeneous;    Hard potentials;    Hard spheres;    Long-range interactions;    Measure solution;    Moment estimate;    Moment production;    Exponential moment;    Stability estimate;    Mehler transform;   

DOI  :  10.1016/j.jde.2011.10.021

来源: Elsevier

【 摘 要 】

The spatially homogeneous Boltzmann equation with hard potentials is considered for measure valued initial data having finite mass and energy. We prove the existence of weak measure solutions, with and without angular cutoff on the collision kernel: the proof in particular makes use of an approximation argument based on the Mehler transform. Moment production estimates in the usual form and in the exponential form are obtained for these solutions. Finally for the Grad angular cutoff, we also establish uniqueness and strong stability estimate on these solutions. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free