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SUMMARY:Free boundaries in certain incompressible flows
DTSTART;VALUE=DATE-TIME:20190617T080000Z
DTEND;VALUE=DATE-TIME:20190617T100000Z
DTSTAMP;VALUE=DATE-TIME:20210731T212149Z
UID:indico-event-4714@indico.math.cnrs.fr
DESCRIPTION:In this course we will talk about several free boundary proble
ms arising in incompressible fluid mechanics\, i.e. an evolutionary partia
l differential equations posed in a moving spatial domain (which is part o
f the unknowns of the problem). This is a hot area of research nowadays. I
n particular we will introduce\n-the vortex patch problem\n-the Muskat pro
blem studying incompressible flow in porous media\n-the water waves proble
m\nFurthermore\, we will also derive and study asymptotic models for the m
oving interfaces in some of the previous scenarios.\n\n \n\n\nLesson 1: I
ntroduction of the Euler equations for incompressible fluids. Introduction
of the Darcy's law. Introduction of the vorticity formulation. Active sca
lars. Introduction of the free boundary problems for active scalars. Intro
duction of the water waves problem. Comparison between the vortex patch pr
oblem\, the Muskat problem and the water waves problem.\n\n\nhttps://indic
o.math.cnrs.fr/event/4714/
LOCATION:Bâtiment Braconnier Salle 125
URL:https://indico.math.cnrs.fr/event/4714/
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