On measure solutions of the Boltzmann equation, part I: Moment production and stability estimates
Accepted version
Peer-reviewed
Repository URI
Repository DOI
Change log
Authors
Lu, XG
Mouhot, C
Abstract
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.
Description
Keywords
Boltzmann equation, Spatially homogeneous, Hard potentials, Hard spheres, Long-range interactions, Measure solution, Moment estimate, Moment production, Exponential moment, Stability estimate, Mehler transform, SPATIALLY HOMOGENEOUS BOLTZMANN, LONG-RANGE INTERACTIONS, ANGULAR SINGULARITY, UNIQUENESS, ENERGY, INEQUALITIES, CONVERGENCE, EQUILIBRIUM, POTENTIALS
Journal Title
J DIFFER EQUATIONS
Conference Name
Journal ISSN
0022-0396
Volume Title
252
Publisher
Elsevier BV