On Measure Solutions of the Boltzmann Equation, part I: Moment Production and Stability Estimates

Details On Measure Solutions of the Boltzmann Equation, part I: Moment Production and Stability Estimates On Measure Solutions of the Boltzmann Equation, part I: Moment Production and Stability Estimates

2011-02-02

arxiv.org/abs/1102.0373v2

Journal of Differential Equations 252, 4 (2012) 3305-3363

Mathematics

Analysis of PDEs

New version: many typos corrected, and more explanations added. 51 pages, to appear in J. Diff. Eq

Scientific paper

10.1016/j.jde.2011.10.021

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 \emph{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.

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