On a Model Boltzmann Equation without Angular Cutoo 1

On the Singularities of the Global Small Solutions of the Full Boltzmann Equation

We show how the singularities are propagated for the (spatially homogeneous) Boltzmann equation (with the usual angular cutoo of Grad) in the context of the small solutions rst introduced by Kaniel and Shinbrot.

On the Smoothing Properties of a Model Boltzmann Equation without Grad's Cutoo Assumption

About L P Estimates for the Spatially Homogeneous Boltzmann Equation

For the homogeneous Boltzmann equation with (cutoo or non cutoo) hard potentials, we prove estimates of propagation of L p norms with a weight (1+jxj 2) q=2 (1 < p < +1, q 2 R large enough), as well as appearance of such weights. The proof is based on some new functional inequalities for the collision operator, proven by elementary means.

The Gevrey Hypoellipticity for Linear and Non-linear Fokker-planck Equations

Recently, a lot of progress has been made on the study for the spatially homogeneous Boltzmann equation without angular cutoff, cf. [2, 3, 8, 22] and references therein, which shows that the singularity of collision cross-section yields some gain of regularity in the Sobolev space frame on weak solutions for Cauchy problem. That means, this gives the C regularity of weak solution for the spatia...

Global hypoelliptic and symbolic estimates for the linearized Boltzmann operator without angular cutoff

In this article we provide global subelliptic estimates for the linearized inhomogeneous Boltzmann equation without angular cutoff, and show that some global gain in the spatial direction is available although the corresponding operator is not elliptic in this direction. The proof is based on a multiplier method and the so-called Wick quantization, together with a careful analysis of the symbol...