The Boltzmann equation without angular cutoff in the whole space: I, an essential coercivity estimate

Radjesvarane Alexandre (1) , Y. 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 department of mathematics

It is known that the singularity in the non-cutoff cross-section of the Boltzmann equation leads to the gain of regularity and gain of weight in the velocity variable. By defining and analyzing a non-isotropy norm which precisely captures the dissipation in the linearized collision operator, we give a new and precise coercivity estimate for the non-cutoff Boltzmann equation for general physical cross sections.

Mots clés: coercivity estimate; Boltzmann equation; non-cutoff cross-sections; non-isotropic norm; coercivity estimate.

Domaines: Equations aux dérivées partielles [math.AP]

Radjesvarane Alexandre, Y. Morimoto, Seiji Ukai, Chao-Jiang Xu, Tong Yang. The Boltzmann equation without angular cutoff in the whole space: I, an essential coercivity estimate. 2010. ⟨hal-00477662v1⟩