Analysis Seminar

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The Landau equation does not blow up

Speaker: Nestor Guillen, Texas State University

Location: Warren Weaver Hall 1302

Date: Thursday, March 7, 2024, 11 a.m.

Synopsis:

We consider solutions to the space-homogeneous Landau equation with a general family of interaction potentials. We prove that their Fisher information is monotone decreasing in time. The class of interaction potentials covered by our result includes the case of the Landau equation with Coulomb interactions. As a consequence of the global boundedness of the Fisher information, we deduce that solutions to the space-homogeneous Landau equation never blow up. This is a joint work with Luis Silvestre.