University of Heidelberg, Applied Analysis Seminar
Thu 23.04.2020
14:15, posted in Applied Analysis

Abstract:
While under the so called Grad cutoff assumption the homogeneous Boltzmann equation is known to propagate smoothness and singularities, it has long been suspected that the non-cutoff Boltzmann operator has similar coercivity properties as a fractional Laplace operator. This has led to the hope that the homogenous Boltzmann equation enjoys similar smoothing properties as the heat equation with a fractional Laplacian. We prove that any weak solution of the fully nonlinear non-cutoff homogenous Boltzmann equation (for Maxwellian molecules) with initial datum of finite mass, energy, and entropy immediately becomes Gevrey regular for strictly positive times.

(Joint work with Jean-Marie Barbaroux, Dirk Hundertmark, and Semjon Vugalter)

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