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Seminar

Water waves and other interface problems (Part 1): Entropies of free surface flows in fluid dynamics May 18, 2021 (08:00 AM PDT - 09:00 AM PDT)
Parent Program:
Location: SLMath: Online/Virtual
Speaker(s) Thomas Alazard (Ecole Normale Supérieure Paris-Saclay; Centre National de la Recherche Scientifique (CNRS))
Description

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

Keywords and Mathematics Subject Classification (MSC)
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

Entropies of Free Surface Flows in Fluid Dynamics
Abstract/Media

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

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. 

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Entropies of Free Surface Flows in Fluid Dynamics