University of Heidelberg, **Applied Analysis Seminar**

Dr. Tobias Ried (MPI MIS, Leipzig)

Online talk - Gevrey smoothing of weak solutions of the homogeneous Boltzmann equation

Online talk - Gevrey smoothing of weak solutions of the homogeneous Boltzmann equation

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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