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SUMMARY:Global Stability of Solutions to a Beta-Plane Equation
DTSTART;VALUE=DATE-TIME:20171114T141500Z
DTEND;VALUE=DATE-TIME:20171114T151500Z
DTSTAMP;VALUE=DATE-TIME:20180717T190759Z
UID:indico-event-2438@indico.math.cnrs.fr
DESCRIPTION:We study the motion of an incompressible\, inviscid two-dimens
ional fluid in a rotating frame of reference. There the fluid experiences
a Coriolis force\, which we assume to be linearly dependent on one of the
coordinates. This is a common approximation in geophysical fluid dynamics
and is referred to as beta-plane. In vorticity formulation the model we co
nsider is then given by the Euler equation with the addition of a linear a
nisotropic\, non-degenerate\, dispersive term. This allows us to treat the
problem as a quasilinear dispersive equation whose linear solutions exhib
it decay in time at a critical rate.\nOur main result is the global stabil
ity and decay to equilibrium of sufficiently small and localized solutions
. Key aspects of the proof are the exploitation of a “double null form
” that annihilates interactions between waves with parallel frequencies
and a Lemma for Fourier integral operators\, which allows us to control a
strong weighted norm and is based on a non-degeneracy property of the nonl
inear phase function associated with the problem.\n\nJoint work with Fabio
Pusateri\; prior work with Tarek Elgindi.\n\nhttps://indico.math.cnrs.fr/
event/2438/
LOCATION:Université Claude Bernard Lyon 1 - Campus de la Doua\, Bâtiment
Braconnier Fokko Du Cloux
URL:https://indico.math.cnrs.fr/event/2438/
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