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Room P3.10, Mathematics Building
David Lannes, Université Bordeaux I
Well-Posedness of the Water-Waves Equations
The water-waves problem consists in finding the motion of the free
surface of a perfect, incompressible and irrotational fluid under
the influence of gravity. Such a motion is described by the Euler
Equations with free surface. I will propose a proof of the
well-posedness of these equations, which is quite elementary. I
will comment on various of the tools involved in the proof:
Dirichlet-to-Neuman operators, regularizing diffeomorphisms, shape
optimization, Nash-Moser iterative scheme, etc.