Ultra-analytic effect of Cauchy problem for a class of kinetic equations

Details Ultra-analytic effect of Cauchy problem for a class of kinetic equations Ultra-analytic effect of Cauchy problem for a class of kinetic equations

2009-03-22

arxiv.org/abs/0903.3703v1

J. Differential Equations 247 (2009) 597-617

Mathematics

Analysis of PDEs

22 pages, to appear in JDE

Scientific paper

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.

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