非弹性Kac方程的正则性

Regularity of the inelastic Kac equation

研究Kac-Boltzmann型方程,对满足动量、能量有限的解,给出在任何时间区间[δ,T](0,∞)上的加权L1,L2估计,并利用这些结果,建立方程解的正则性。

In this paper ,we study the Kac-Boltzmann equation.Firstly,the Povzner inequality for the collision kernel and the LP estimates for the collision operator are established.Secondly,we obtain some weighted LP estimates for positive solutions to the equation.With these estimates,the smoothness of the solutions are proved.