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

作者：Morimoto Yoshinori; Xu Chao Jiang

来源：Journal of Differential Equations, 2009, 247(2): 596-617.

DOI：10.1016/j.jde.2009.01.028

• Landau equation
• Fokker-Planck equation
• Ultra-analytic effect of Cauchy problem

The smoothing effect of the Cauchy problem for a class of kinetic equations is studied. We firstly consider the spatially homogeneous nonlinear 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.

• 出版日期2009-7-15
• 单位武汉大学