LOCAL EXISTENCE WITH MILD REGULARITY FOR THE BOLTZMANN EQUATION

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

Without Grad's angular cuto assumption, the local existence of classical solutions to the Boltzmann equation is studied. There are two new improvements: the index of Sobolev spaces for the solution is related to the parameter of the angular singularity; moreover, we do not assume that the initial data is close to a global equilibrium. Using the energy method, one important step in the analysis is the study of fractional derivatives of the collision operator and related commutators.

Mots clés: Boltzmann equation; energy estimates; existence of solution; fractional derivatives.

Domaines: Equations aux dérivées partielles [math.AP]

Radjesvarane Alexandre, Yoshinori Morimoto, Seiji Ukai, Chao-Jiang Xu, Tong Yang. LOCAL EXISTENCE WITH MILD REGULARITY FOR THE BOLTZMANN EQUATION. Kinetic and Related Models , 2013, 6 (4), pp.1011-1041. ⟨10.3934/krm.2013.6.1011⟩. ⟨hal-01116718⟩