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math.AP2015★ 5 cited
Strong smoothing for the non-cutoff homogeneous Boltzmann equation for Maxwellian molecules with Debye-Yukawa type interaction
Jean-Marie Barbaroux, Dirk Hundertmark, Tobias Ried +1
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…
math.AP2015★ 21 cited
Gevrey smoothing for weak solutions of the fully nonlinear homogeneous Boltzmann and Kac equations without cutoff for Maxwellian molecules
Jean-Marie Barbaroux, Dirk Hundertmark, Tobias Ried +1
It has long been suspected that the non-cutoff Boltzmann operator has similar coercivity properties as a fractional Laplacian. This has led to the hope that the homogenous Boltzman…