PHASE SPACE ANALYSIS AND FUNCTIONAL CALCULUS FOR THE LINEARIZED LANDAU AND BOLTZMANN OPERATORS

Nicolas Lerner (1) , Yoshinori Morimoto (2) , Karel Pravda-Starov (3) , Chao-Jiang Xu (4)

1 IMJ - Institut de Mathématiques de Jussieu
2 Graduate School of Human and Environmental Studies
3 IRMAR - Institut de Recherche Mathématique de Rennes
4 LMRS - Laboratoire de Mathématiques Raphaël Salem

We prove that the linearized non-cuto Boltzmann operator with Maxwellian molecules is exactly equal to a fractional power of the linearized Landau operator which is the sum of the harmonic oscillator and the spherical Laplacian. This result allows to display explicit sharp coercive estimates satis- ed by the linearized non-cuto Boltzmann operator for both Maxwellian and non-Maxwellian molecules.

Mots clés: Boltzmann operator; Landau operator; spectral analysis; anisotropy; microlocal analysis.

Domaines: Equations aux dérivées partielles [math.AP]

Nicolas Lerner, Yoshinori Morimoto, Karel Pravda-Starov, Chao-Jiang Xu. PHASE SPACE ANALYSIS AND FUNCTIONAL CALCULUS FOR THE LINEARIZED LANDAU AND BOLTZMANN OPERATORS. Kinetic and Related Models , 2013, 6 (3), pp.625-648. ⟨10.3934/krm.2013.6.625⟩. ⟨hal-01116722⟩