On the uniqueness for the spatially homogeneous Boltzmann equation with a strong angular singularity

Details On the uniqueness for the spatially homogeneous Boltzmann equation with a strong angular singularity On the uniqueness for the spatially homogeneous Boltzmann equation with a strong angular singularity

2007-10-12

arxiv.org/abs/0710.2460v1

Mathematics

Analysis of PDEs

Scientific paper

10.1007/s10955-008-9511-5

We prove an inequality on the Wasserstein distance with quadratic cost between two solutions of the spatially homogeneous Boltzmann equation without angular cutoff, from which we deduce some uniqueness results. In particular, we obtain a local (in time) well-posedness result in the case of (possibly very) soft potentials. A global well-posedeness result is shown for all regularized hard and soft potentials without angular cutoff. Our uniqueness result seems to be the first one applying to a strong angular singularity, except in the special case of Maxwell molecules. Our proof relies on the ideas of Tanaka: we give a probabilistic interpretation of the Boltzmann equation in terms of a stochastic process. Then we show how to couple two such processes started with two different initial conditions, in such a way that they almost surely remain close to each other.

Affiliated with

Also associated with

No associations

Rating

On the uniqueness for the spatially homogeneous Boltzmann equation with a strong angular singularity 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 On the uniqueness for the spatially homogeneous Boltzmann equation with a strong angular singularity, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the uniqueness for the spatially homogeneous Boltzmann equation with a strong angular singularity will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-403719