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

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

doi:10.3934/krm.2017036

Article Contents

2017, Volume 10, Issue 4: 901-924. Doi: 10.3934/krm.2017036

This issue Previous Article Entropy-based mixed three-moment description of fermionic radiation transport in slab and spherical geometries Next Article Boundary layers for discrete kinetic models: Multicomponent mixtures, polyatomic molecules, bimolecular reactions, and quantum kinetic equations

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

1.
Aix Marseille Univ, Université de Toulon, CNRS, CPT, Marseille, France
2.
Institute for Analysis, Karlsruhe Institute of Technology (KIT), Englerstraße 2,76131 Karlsruhe, Germany

Received: December 2015

Revised: November 2016

Published: December 2017

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Abstract

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.

Keywords:

Smoothing of weak solutions,
non-cutoff homogeneous Boltzmann equation,
Debye-Yukawa potential,
Maxwellian molecules.

Mathematics Subject Classification: Primary: 35D10; Secondary: 35B65, 35Q20, 82B40.

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References

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