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Free boundaries in certain incompressible flows (1/5)
(Universidad de Cantabria)
Salle 125 (Bâtiment Braconnier)
ICJ,UCBL, Bâtiment Braconnier
Campus de la Doua
In this course we will talk about several free boundary problems arising in incompressible fluid mechanics, i.e. an evolutionary partial differential equations posed in a moving spatial domain (which is part of the unknowns of the problem). This is a hot area of research nowadays. In particular we will introduce
-the vortex patch problem
-the Muskat problem studying incompressible flow in porous media
-the water waves problem
Furthermore, we will also derive and study asymptotic models for the moving interfaces in some of the previous scenarios.
Lesson 1: Introduction of the Euler equations for incompressible fluids. Introduction of the Darcy's law. Introduction of the vorticity formulation. Active scalars. Introduction of the free boundary problems for active scalars. Introduction of the water waves problem. Comparison between the vortex patch problem, the Muskat problem and the water waves problem.