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