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

Lu, Xuguang; Mouhot, Clément

Lu, Xuguang; Mouhot, Clément (2012), On Measure Solutions of the Boltzmann Equation, part I: Moment Production and Stability Estimates, Journal of Differential Equations, 252, 4, p. 3305-3363. http://dx.doi.org/10.1016/j.jde.2011.10.021

Type

Article accepté pour publication ou publié

External document link

http://arxiv.org/abs/1102.0373v2

Date

2012

Journal name

Journal of Differential Equations

Volume

252

Number

Publisher

Elsevier

Pages

3305-3363

Abstract (EN)

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.

Subjects / Keywords

Boltzmann equation; spatially homogeneous; hard potentials; hard spheres; long-range interactions; measure solution; moment estimate; moment production; exponential moment; stability estimate; Mehler transform