Smoothing effect of weak solutions for the spatially homogeneous   Boltzmann Equation without angular cutoff
  In this paper, we consider the spatially homogeneous Boltzmann equation without angular cutoff. We prove that every $L^1$ weak solution to the Cauchy problem with finite moments of all order acquires the $C^\infty$ regularity in the velocity variable for the positive time. 
Radjesvarane Alexandre (IRENAV), Yoshinori Morimoto, Seiji Ukai (Mr.),   Chao-Jiang Xu (LMRS), Tong Yang (Pr.)
math.AP