Distributional and classical solutions to the Cauchy Boltzmann problem for soft potentials with integrable angular cross section

Details Distributional and classical solutions to the Cauchy Boltzmann problem for soft potentials with integrable angular cross section Distributional and classical solutions to the Cauchy Boltzmann problem for soft potentials with integrable angular cross section

2009-02-18

arxiv.org/abs/0902.3106v3

Journal of Statistical Physics, V 137, Numbers 5-6, 1147 - 1165 (2009)

Physics

Mathematical Physics

19 pages

Scientific paper

This paper focuses on the study of existence and uniqueness of distributional and classical solutions to the Cauchy Boltzmann problem for the soft potential case assuming $S^{n-1}$ integrability of the angular part of the collision kernel (Grad cut-off assumption). For this purpose we revisit the Kaniel--Shinbrot iteration technique to present an elementary proof of existence and uniqueness results that includes large data near a local Maxwellian regime with possibly infinite initial mass. We study the propagation of regularity using a recent estimate for the positive collision operator given in [3], by E. Carneiro and the authors, that permits to study such propagation without additional conditions on the collision kernel. Finally, an $L^{p}$-stability result (with $1\leq p\leq\infty$) is presented assuming the aforementioned condition.

Affiliated with

Also associated with

No associations

Rating

Distributional and classical solutions to the Cauchy Boltzmann problem for soft potentials with integrable angular cross section 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 Distributional and classical solutions to the Cauchy Boltzmann problem for soft potentials with integrable angular cross section, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Distributional and classical solutions to the Cauchy Boltzmann problem for soft potentials with integrable angular cross section will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-128151