THE BOLTZMANN EQUATION WITHOUT ANGULAR CUTOFF IN THE WHOLE SPACE: II, GLOBAL EXISTENCE FOR HARD POTENTIAL

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

As a continuation of our series works on the Boltzmann equation without angular cutoff assumption, in this part, the global existence of solution to the Cauchy problem in the whole space is proved in some suitable weighted Sobolev spaces for hard potential when the solution is a small perturbation of a global equilibrium.

Mots clés: Boltzmann equation; non-cutoff hard potentials; global existence

Domaines: Equations aux dérivées partielles [math.AP]

Radjesvarane Alexandre, Yoshinori Morimoto, Seiji Ukai, Chao-Jiang Xu, Tong Yang. THE BOLTZMANN EQUATION WITHOUT ANGULAR CUTOFF IN THE WHOLE SPACE: II, GLOBAL EXISTENCE FOR HARD POTENTIAL. Analysis and Applications, 2011, 9 (2), pp.113-134. ⟨10.1142/S0219530511001777⟩. ⟨hal-01116725⟩