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December  2017, 10(4): 901-924. doi: 10.3934/krm.2017036

## 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  March 2017

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.

Citation: 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 & Related Models, 2017, 10 (4) : 901-924. doi: 10.3934/krm.2017036
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##### References:
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