Ultra-analytic effect of Cauchy problem for a class of kinetic equations
Analysis of PDEs
2009-11-21 v1
Abstract
The smoothing effect of the Cauchy problem for a class of kinetic equations is studied. We firstly consider the spatially homogeneous non linear Landau equation with Maxwellian molecules and inhomogeneous linear Fokker-Planck equation to show the ultra-analytic effects of the Cauchy problem. Those smoothing effect results are optimal and similar to heat equation. In the second part, we study a model of spatially inhomogeneous linear Landau equation with Maxwellian molecules, and show the analytic effect of the Cauchy problem.
Keywords
Cite
@article{arxiv.0903.3703,
title = {Ultra-analytic effect of Cauchy problem for a class of kinetic equations},
author = {Yoshinori Morimoto and Chao-Jiang Xu},
journal= {arXiv preprint arXiv:0903.3703},
year = {2009}
}
Comments
22 pages, to appear in JDE