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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References:

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