Online Analysis and PDE seminar (UAM-UC-UC3M-UCM-ICMAT-IMUS)

Conferenciante: Eduardo García-Juárez, U. de Barcelona

Fecha: Miércoles 6 de abril de 2022 - 15:00

Enlace al seminario

Resumen: The Peskin problem models the dynamics of a closed elastic membrane immersed in an incompressible Stokes fluid. This set of equations was proposed as a simplified model for the motion of red blood cells and it serves as a canonical test problem for numerical methods. Studying the well-posedness of the problem is necessary to perform numerical analysis and to guarantee that numerical methods based upon different formulations of the problem converge to the same solution. Mathematically, the problem can be seen as a generalization of the Stokes two-phase interface with surface tension, and shares the linear structure with the Muskat problem. We will review some of the latest well-posedness problems, and in particular we will focus on the global regularity issue for 2D Peskin with viscosity jump and the local well-posedness for 3D membranes.