Global hypoelliptic and symbolic estimates for the linearized Boltzmann operator without angular cutoff

Radjesvarane Alexandre (1) , Frédéric Hérau (2) , Wei-Xi Li (3)

1 USTH - University of Science and Technology of Hanoi
2 LMJL - Laboratoire de Mathématiques Jean Leray
3 School of Mathematics and Statistics [Wuhan]

In this article we provide global subelliptic estimates for the linearized inhomogeneous Boltzmann equation without angular cutoff, and show that some global gain in the spatial direction is available although the corresponding operator is not elliptic in this direction. The proof is based on a multiplier method and the so-called Wick quantization, together with a careful analysis of the symbolic properties of the Weyl symbol of the Boltzmann collision operator.

Mots clés: subellipticity; global hypoellipticity; anisotropic diffusion; Boltzmann equation without cutoff; Wick quantization; Boltzmann equation without cut-off

Domaines: Equations aux dérivées partielles [math.AP]

Radjesvarane Alexandre, Frédéric Hérau, Wei-Xi Li. Global hypoelliptic and symbolic estimates for the linearized Boltzmann operator without angular cutoff. 2017. ⟨hal-00766817v5⟩