Strong smoothing for the non-cutoff homogeneous Boltzmann equation for Maxwellian molecules with Debye-Yukawa type interaction. (English) Zbl 1364.35230

Barbaroux, Jean-Marie; Hundertmark, Dirk; Ried, Tobias; Vugalter, Semjon

Kinet. Relat. Models 10, No. 4, 901-924 (2017).

Summary: 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.

MSC:

35Q20	Boltzmann equations
35B65	Smoothness and regularity of solutions to PDEs
82B40	Kinetic theory of gases in equilibrium statistical mechanics
35D30	Weak solutions to PDEs

Keywords:

smoothing of weak solutions; non-cutoff homogeneous Boltzmann equation; Debye-Yukawa potential; Maxwellian molecules

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