Global stability of the Boltzmann equation nearby equilibrium

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• Bob Strain (University of Pennsylvania)
• Monday 24 May 2010, 16:00-17:00
• CMS, MR13.

If you have a question about this talk, please contact Prof. Mihalis Dafermos.

The Boltzmann equation has been a cornerstone of statistical physics for about 140 years, but because of the extremely singular nature of the Boltzmann collision operator, the tools necessary for rigorous study of this equation (without relying on the so-called “Grad cutoff” assumption) have only recently emerged. This central equation provides a basic example where a wide range of geometric fractional derivatives occur in a physical model of the natural world.

We explain our recent proof of global stability for the Boltzmann equation 1872 with the physically important collision kernels derived by Maxwell 1867 for the full range of inverse power intermolecular potentials, r^{-(p-1)} with p > 2 and more generally. Our solutions are perturbations of the Maxwellian equilibrium states, and they decay rapidly in time to equilibrium as predicted by celebrated the Boltzmann H-theorem.

This is joint work with P. Gressman.

This talk is part of the Partial Differential Equations seminar series.

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