Cooling process for inelastic Boltzmann equations for hard spheres, Part I: The Cauchy problem

Details Cooling process for inelastic Boltzmann equations for hard spheres, Part I: The Cauchy problem Cooling process for inelastic Boltzmann equations for hard spheres, Part I: The Cauchy problem

2006-07-21

arxiv.org/abs/math/0607535v1

Journal of Statistical Physics 124 (2006) 655-702

Mathematics

Analysis of PDEs

45 pages

Scientific paper

10.1007/s10955-006-9096-9

We develop the Cauchy theory of the spatially homogeneous inelastic Boltzmann equation for hard spheres, for a general form of collision rate which includes in particular variable restitution coefficients depending on the kinetic energy and the relative velocity as well as the sticky particles model. We prove (local in time) non-concentration estimates in Orlicz spaces, from which we deduce weak stability and existence theorem. Strong stability together with uniqueness and instantaneous appearance of exponential moments are proved under additional smoothness assumption on the initial datum, for a restricted class of collision rates. Concerning the long-time behaviour, we give conditions for the cooling process to occur or not in finite time.

Affiliated with

Also associated with

No associations

Rating

Cooling process for inelastic Boltzmann equations for hard spheres, Part I: The Cauchy problem does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Cooling process for inelastic Boltzmann equations for hard spheres, Part I: The Cauchy problem, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Cooling process for inelastic Boltzmann equations for hard spheres, Part I: The Cauchy problem will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-169821