期刊
JOURNAL OF DIFFERENTIAL EQUATIONS
卷 252, 期 4, 页码 3305-3363出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jde.2011.10.021
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
类别
资金
- National Natural Science Foundation of China [10571101]
- University Paris-Dauphine
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.
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