STRONG SMOOTHING FOR THE NON-CUTOFF HOMOGENEOUS BOLTZMANN EQUATION FOR MAXWELLIAN MOLECULES WITH DEBYE-YUKAWA TYPE INTERACTION

被引：5

作者：

Barbaroux, Jean-Marie ^{[1
]}

Hundertmark, Dirk ^{[2
]}

Ried, Tobias ^{[2
]}

Vugalter, Semjon ^{[2
]}

机构：

[1] Aix Marseille Univ, Univ Toulon, CNRS, CPT, Marseille, France

[2] Karlsruhe Inst Technol, Inst Anal, Englerstra 2, D-76131 Karlsruhe, Germany

来源：

关键词：

Smoothing of weak solutions; non-cutoff homogeneous Boltzmann equation; Debye-Yukawa potential; Maxwellian molecules; REGULARITY; RANGE;

D O I：

10.3934/krm.2017036

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：901 / 924

页数：24

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