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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Boltzmann flowsÂ in a general framework: from the
classical\, to gas mixtures\, to polyatomic gases
Part 1 - Irene M. Gamba (University of Texas at Au
stin)
DTSTART;TZID=Europe/London:20220510T133000
DTEND;TZID=Europe/London:20220510T141500
UID:TALK172538AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/172538
DESCRIPTION:We will discuss in the fundamental functional feat
ures of scalar and systems of Boltzmann type flow.
Binary interaction laws enable an existence and u
niqueness theory for scalar or arbitrary systems m
odeling polyatomic gases or mixtures of gas partic
les with different masses\, even as the BEC stabil
ity for quantum Boltzmann-condensation system mode
ls fell into a rather unified way after good momen
ts and a priori estimates are obtained. From an an
alytical viewpoint\, the crucial study lies in the
identification of a Banach space associated to th
e interactions and their collision frequency chara
cterized by the transition probability rates of ho
pping interacting particle pairs. This approach ex
pands from the problem and initial data to yield u
pper and lower bounds and coerciveness that plays
a crucial role in stability and longterm behavior
of the system \; arising from \; solutions
to ODEs in Banach spaces. In addition\, the obtai
ned estimates provide the ground to obtain a $W^{p
\,s}$- polynomial and exponentially weighted Sobol
ev regularity to solutions of these types of Boltz
mann flows. These results do not depend on entropy
estimates\, yet if the initial entropy is bounded
\, then it will remain bounded depending on the in
itial invariant moments\, for all times. Moreover\
, since these estimates yield sufficient condition
s to control the high energy tail decay that sets
a framework for the calculations to time decay rat
e to equilibrium for Boltzmann equation types\, ho
mogeneous in space\, or with periodic boundary con
ditions\, or with \; boundary conditions corre
sponding to zero flux across boundaries. This is w
ork in different collaborations with Ricardo Alons
o\, Erica de la Canal and Milana Pavic-Colic.
LOCATION:Seminar Room 2\, Newton Institute
CONTACT:
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