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SUMMARY:Cercignani's conjecture between multiples of the equilibrium - Jos
 é A. Cañizo\, Granada University 
DTSTART:20150126T150000Z
DTEND:20150126T160000Z
UID:TALK57147@talks.cam.ac.uk
CONTACT:Amit Einav
DESCRIPTION:The question of whether there exists a functional inequality t
 hat bounds the relative entropy by its production rate in the Boltzmann eq
 uation is known as Cercignani's conjecture. One of the reasons it is inter
 esting 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 cond
 itions: we show that Cercignani's conjecture holds on the set S of all fun
 ctions with fixed invariants (mass\, energy and momentum) and which are bo
 unded above and below by two fixed multiples of the equilibrium Maxwellian
  distribution (the one with the same invariants). We will also present som
 e 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.
LOCATION:CMS\, MR13
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