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CIRM – Centre International de Rencontres Mathématiques

Our project focuses on understanding the interplay between elasticity and the classical Hele-Shaw model, with the long-term of simplifying the model and improving its suitability for numerical applications and algorithmic development. Our first aim is to show existence of solutions via the convergence of an implicit time-discretization using the Wasserstain distance. We expect the limit to satisfy the equation in a distributional sense as well as an optimal energy-dissipation relation. Similarly, we construct weak solutions to the Cahn-Hilliard equation with degenerate mobility and elastic misfits. Finally, we aim to prove that the sharp interface limit is a distributional solution to the elastically modified Hele–Shaw flow with optimal energy-dissipation rate.

CIRM – Centre International de Rencontres Mathématiques

The school will introduce participants to several hot research topics at the frontier between geophysical fluid dynamics, fundamental physics and mathematics. The main themes will be spontaneous stochasticity, waves in geophysical and astrophysical fluids and fundamental challenges in hydrodynamic and wave turbulence. The school will consist of several lecture series, plus a number of research seminars, covering mathematical, theoretical and experimental aspects. The school is organized in the framework of an international collaboration which started in 2019 and which is financially supported by the Simons Foundation (https://cims.nyu.edu/wave-turbulence/people/). This “Simons Collaboration on Wave Turbulence” brings together physicists and mathematicians with the aim of addressing fundamental questions about the Wave Turbulence theory and its applicability to real systems and especially to the Earth climate system.

Courses and Events for Math Students and Early Career Researchers,    Applied Mathematics (in general)