Strong smoothing for the non-cutoff homogeneous Boltzmann equation for Maxwellian molecules with Debye-Yukawa type interaction

Jean-Marie Barbaroux (1, 2) , Dirk Hundertmark (3) , Tobias Ried (3) , Semjon Vugalter (3)

1 CPT - E8 Dynamique quantique et analyse spectrale
2 CPT - Centre de Physique Théorique - UMR 7332
3 KIT - Karlsruhe Institute of Technology

We study weak solutions of the homogeneous Boltzmann equation for Maxwellian molecules with a logarithmic singularity of the collision kernel for grazing collisions. Even though in this situation the Boltzmann operator enjoys only a very weak coercivity estimate, it still leads to strong smoothing of weak solutions in accordance to the smoothing expected by an analogy with a logarithmic heat equation.

Mots clés: Debye-Yukawa potential; Smoothing of weak solutions; Non-cutoff homogeneous Boltzmann equation; Maxwellian molecules

Domaines: Physique mathématique [math-ph]; Mathématiques [math]

Jean-Marie Barbaroux, Dirk Hundertmark, Tobias Ried, Semjon Vugalter. Strong smoothing for the non-cutoff homogeneous Boltzmann equation for Maxwellian molecules with Debye-Yukawa type interaction. Kinetic and Related Models , 2017, 10 (4), pp.901-924. ⟨10.3934/krm.2017036⟩. ⟨hal-01253144⟩