Convex integration: from basic tools to Muskat problem.

par Sofiane Cherf (ICJ)

jeudi 19 nov. 2026, 10:00 → 12:00 Europe/Paris

Convex integration is a method to construct wild solutions to nonlinear problems written as differential inclusions by introducing highly oscillatory potentials. In this talk, we will first introduce the main tools and ideas of convex integration exemplified in a simple geometric setting. This technique can be adapted for finding weak regularity solutions for non linear PDEs. We will show how Székelyhidi used it in the case of the Muskat problem, in a paper entitled "Relaxation of the incompressible porous media equation". Finally, still in the case of the Muskat problem, we will discuss the link between the notion of subsolutions in convex integration and the relaxation approach of Otto relying on the underlying Wasserstein gradient flow structure.