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SUMMARY:Boltzmann flows  in a general framework: from the classical\, to g
 as mixtures\, to polyatomic gases - Part 2 - Irene M. Gamba (University of
  Texas at Austin)
DTSTART:20220510T135000Z
DTEND:20220510T143500Z
UID:TALK172541@talks.cam.ac.uk
DESCRIPTION:We will discuss in the fundamental functional features of scal
 ar and systems of Boltzmann type flow. Binary interaction laws enable an e
 xistence and uniqueness theory for scalar or arbitrary systems modeling po
 lyatomic gases or mixtures of gas particles with different masses\, even a
 s the BEC stability for quantum Boltzmann-condensation system models fell 
 into a rather unified way after good moments and a priori estimates are ob
 tained. From an analytical viewpoint\, the crucial study lies in the ident
 ification of a Banach space associated to the interactions and their colli
 sion frequency characterized by the transition probability rates of hoppin
 g interacting particle pairs. This approach expands from the problem and i
 nitial data to yield upper and lower bounds and coerciveness that plays a 
 crucial role in stability and longterm behavior of the system&nbsp\; arisi
 ng from&nbsp\; solutions to ODEs in Banach spaces. In addition\, the obtai
 ned estimates provide the ground to obtain a $W^{p\,s}$- polynomial and ex
 ponentially weighted Sobolev regularity to solutions of these types of Bol
 tzmann flows. These results do not depend on entropy estimates\, yet if th
 e initial entropy is bounded\, then it will remain bounded depending on th
 e initial invariant moments\, for all times. Moreover\, since these estima
 tes yield sufficient conditions to control the high energy tail decay that
  sets a framework for the calculations to time decay rate to equilibrium f
 or Boltzmann equation types\, homogeneous in space\, or with periodic boun
 dary conditions\, or with&nbsp\; boundary conditions corresponding to zero
  flux across boundaries. This is work in different collaborations with Ric
 ardo Alonso\, Erica de la Canal and Milana Pavic-Colic.
LOCATION:Seminar Room 2\, Newton Institute
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