1205.3688 (Nicolas Lerner et al.)

Phase space structure and functional calculus for the linearized Landau
and boltzmann operators    [PDF]

Nicolas Lerner, Yoshinori Morimoto, Karel Pravda-Starov, Chao-Jiang Xu

We study the non-cutoff Boltzmann collision operator and the Landau collision operator linearized around a normalized Maxwellian distribution. For Maxwellian molecules, we prove that the linearized non-cutoff Boltzmann operator is equal to a fractional power of the linearized Landau operator. Furthermore, we provide the exact anisotropic phase space structure of these two linearized operators and display the sharp anisotropic coercive estimates satisfied by the linearized non-cutoff Boltzmann operator for both Maxwellian and non-Maxwellian molecules.

View original: http://arxiv.org/abs/1205.3688