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SUMMARY:Partially dissipative systems: hypocoercivity and hyperbolic appro
ximations
DTSTART:20240326T101500Z
DTEND:20240326T111500Z
DTSTAMP:20240414T140500Z
UID:indico-event-10132@indico.math.cnrs.fr
DESCRIPTION:Speakers: TimothÃ©e Crin-Barrat\n\nIn this talk\, we review re
cent results on so-called partially dissipative hyperbolic systems. Such s
ystems model physical phenomena with degenerate dissipative terms and appe
ar in many applications. For example\, in gas dynamics where the mass is c
onserved during the evolution\, but the momentum balance includes a diffus
ion (viscosity) or a damping (relaxation) term.First\, using tools from th
e hypocoercivity theory and precise frequency decompositions\, we derive s
harp stability estimates for linear systems satisfying the Kalman rank con
dition. This linear analysis allows us to establish new global-in-time exi
stence and asymptotic results in a critical regularity framework for nonli
near models.Then\, we interpret partially dissipative systems as hyperboli
c approximations of parabolic systems\, in the context of the paradox of i
nfinite speed of propagation. In particular\, we focus on a hyperbolic app
roximation of the multi-dimensional compressible Navier-Stokes-Fourier sys
tem and establish its hyperbolic-parabolic strong relaxation limit.\n\nhtt
ps://indico.math.cnrs.fr/event/10132/
LOCATION:Amphi Schwartz (IMT)
URL:https://indico.math.cnrs.fr/event/10132/
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