Smoothing effect of weak solutions for the spatially homogeneous Boltzmann Equation without angular cutoff

Radjesvarane Alexandre (1) , Yoshinori Morimoto (2) , Seiji Ukai (3) , Chao-Jiang Xu (4) , Tong Yang (5)

1 IRENAV - Institut de Recherche de l'Ecole Navale
2 Graduate School of Human and Environmental Studies
3 Mr. - retaite
4 LMRS - Laboratoire de Mathématiques Raphaël Salem
5 Pr. - Department of mathematics

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.

Mots clés: smoothing effect; Boltzmann equation; weak solution; smoothing effect.

Domaines: Equations aux dérivées partielles [math.AP]

Radjesvarane Alexandre, Yoshinori Morimoto, Seiji Ukai, Chao-Jiang Xu, Tong Yang. Smoothing effect of weak solutions for the spatially homogeneous Boltzmann Equation without angular cutoff. J. Math. Kyoto Univ., 2012, 52 (3), pp.433-463. ⟨hal-00589563⟩