Cercignani's conjecture between multiples of the equilibrium

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• José A. Cañizo, Granada University
• Monday 26 January 2015, 15:00-16:00
• CMS, MR13.

If you have a question about this talk, please contact Amit Einav.

The question of whether there exists a functional inequality that bounds the relative entropy by its production rate in the Boltzmann equation is known as Cercignani’s conjecture. One of the reasons it is interesting is that it gives important information on the asymptotic behaviour of the equation. Unfortunately, it is known not to hold in general, even if one imposes quite strong conditions on the set of functions for which it is sought. We present a result that tests this on extremely strong conditions: we show that Cercignani’s conjecture holds on the set S of all functions with fixed invariants (mass, energy and momentum) and which are bounded above and below by two fixed multiples of the equilibrium Maxwellian distribution (the one with the same invariants). We will also present some work in progress towards deducing some consequences on the behaviour of solutions to the space-homogeneous Boltzmann equation, the most important difficulty for this being that this set S is not known to be invariant by the flow of the equation.

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

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