Regularity of solutions for spatially homogeneous Boltzmann equation without angular cutoff : non Maxwellian molecule type (Mathematical Analysis in Fluid and Gas Dynamics)

On the contrary, when the singularity in s is removed, that is, when Grad's \angular cuto assumption" is made (cf. [Gr]), (in other words, when B 2 L 1 loc ( R 3 S 2 )),

We prove an inequality on the Kantorovich-Rubinstein distance – which can be seen as a particular case of a Wasserstein metric– between two solutions of the spatially

R. This is a continuation of our series of works for the inhomogeneous Boltzmann equation. We study qual- itative properties of classical solutions, precisely, the full

Finally, we would like to mention that there are also some interesting results on the uniqueness for the spatially homogeneous Boltzmann equation, for example, for the Maxweillian

Based on this estimation, together with Part II [9], we will prove the global existence of classical non-negative solutions to the Boltzmann equation without angular cutoff, for

The main purpose of this paper is to show the smoothing effect of the spatially homogeneous Boltzmann equation, that is, any weak solution to the Cauchy prob- lem (1.1)

Furthermore, we apply the similar analytic technique for the Sobolev space regularity to the nonlinear equation, and prove the smoothing property of solutions for the

For the non cutoff radially symmetric homogeneous Boltzmann equation with Maxwellian molecules, we give the nu- merical solutions using symbolic manipulations and spectral