Entropies of free surface flows in fluid dynamics

Abstract: I will discuss recent works with Didier Bresch, Nicolas Meunier and Didier Smets about the dynamics of a free surface transported by an incompressible flow obeying Darcy’s law. I will consider the Hele-Shaw and Mullins-Sekerka equations, as well as the thin-film and Boussinesq equations. For these equations, I will present monotonicity properties of different natures : maximum principles, Lyapunov functionals and entropies. The analysis is based on exact identities which in turn allow to study the Cauchy problem for classical solutions in any subcritical Sobolev spaces.

analysis of PDEs

Audience: researchers in the topic

Comments: Here is the poster of this talk: www.dropbox.com/s/3ixoc26oxs2tblj/9th%20PDE%20Seminar.pdf?dl=0

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