Global existence and full regularity of the Boltzmann equation without angular cutoff

Details Global existence and full regularity of the Boltzmann equation without angular cutoff Global existence and full regularity of the Boltzmann equation without angular cutoff

2009-12-08

arxiv.org/abs/0912.1426v3

Mathematics

Analysis of PDEs

Scientific paper

We prove the global existence and uniqueness of classical solutions around an equilibrium to the Boltzmann equation without angular cutoff in some Sobolev spaces. In addition, the solutions thus obtained are shown to be non-negative and $C^\infty$ in all variables for any positive time. In this paper, we study the Maxwellian molecule type collision operator with mild singularity. One of the key observations is the introduction of a new important norm related to the singular behavior of the cross section in the collision operator. This norm captures the essential properties of the singularity and yields precisely the dissipation of the linearized collision operator through the celebrated H-theorem.

Affiliated with

Also associated with

No associations

Rating

Global existence and full regularity of the Boltzmann equation without angular cutoff 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 Global existence and full regularity of the Boltzmann equation without angular cutoff, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Global existence and full regularity of the Boltzmann equation without angular cutoff will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-385538