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SUMMARY:Long-time behavior of the Stokes-transport system in a channel.
DTSTART:20240507T120000Z
DTEND:20240507T141500Z
DTSTAMP:20240529T110500Z
UID:indico-event-10327@indico.math.cnrs.fr
DESCRIPTION:Speakers: Antoine Leblond (Max Planck - Hambourg)\n\nWe consid
er here a 2d incompressible fluid in a periodic channel\, whose density is
advected by pure transport\, and whose velocity is given by the Stokes eq
uation with gravity source term. Dirichlet boundary conditions are taken f
or the velocity field on the bottom and top of the channel\, and periodic
conditions in the horizontal variable. We prove that the affine stratified
density profile is stable under small perturbations in Sobolev spaces and
show convergence of the density to another limiting stratified density p
rofile for large time with an explicit algebraic decay rate. Moreover\, we
are able to precisely identify the limiting profile as the decreasing ver
tical rearrangement of the initial density. Finally\, we show that boundar
y layers are formed for large times in the vicinity of the upper and lower
boundaries. These boundary layers\, which had not been identified in prev
ious works\, are given by a self-similar Ansatz and driven by a linear mec
hanism. This allows us to precisely characterize the long-time behavior be
yond the constant limiting profile and enlighten the optimal decay rate.Th
is is a joint work with Anne-Laure Dalibard and Julien Guillod (Laboratoir
e Jacques-Louis Lions\, Sorbonne Université\, Paris\, France)\, part of m
y PhD thesis. \n\nhttps://indico.math.cnrs.fr/event/10327/
LOCATION:Fokko (ICJ)
URL:https://indico.math.cnrs.fr/event/10327/
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