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SUMMARY:The rigid lid limit for the water waves equation
DTSTART;VALUE=DATE-TIME:20220517T120000Z
DTEND;VALUE=DATE-TIME:20220517T130000Z
DTSTAMP;VALUE=DATE-TIME:20220810T074149Z
UID:indico-event-7548@indico.math.cnrs.fr
DESCRIPTION:The free surface Euler equations or water wave equations model
the evolution of a non viscous fluid under the gravity force\, over a sea
bed and under a free surface that separates the fluid from the air. These
equations capture all the motion of the fluid and are too complicated in g
eneral if one wants to study a specific physical phenomenon. When dealing
with the propagation of large oceanic currents\, oceanographers reasonably
assume that the water surface is flat (still-water level) and use the Eul
er equations in a flat strip as a model. The goal of this talk is to rigor
ously derive this asymptotic regime. We will see that it will lead to a si
ngular limit : the free surface tends to 0 but the time scale also has to
tend +\\infty. The small parameter involved in this regime is the ratio be
tween the amplitude of the typical water waves (that are very small for wa
ve currents) and the typical water depth. First we will explain how we can
get an existence time that is uniform with respect to the small parameter
\, and secondly\, how the physical quantities involved (free surface\, vel
ocity) converge when the small parameter goes to 0. We will see that we ca
n only hope a weak convergence and we will carefully study the lack of str
ong convergence.\n\nhttps://indico.math.cnrs.fr/event/7548/
LOCATION:ICJ Fokko
URL:https://indico.math.cnrs.fr/event/7548/
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