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arXiv · 1512.05134

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
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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.

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Jean-Marie Barbaroux, Dirk Hundertmark, Tobias Ried, Semjon Vugalter. 2015-12-16. Strong smoothing for the non-cutoff homogeneous Boltzmann equation for Maxwellian molecules with Debye-Yukawa type interaction. https://doi.org/10.3934/krm.2017036

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