The Peskin problem models the flow of blood through the heart valves, derived by Charles Peskin to understand the mechanism of valve disease.

This talk will first describe the 2D theory, proving global well-posedness of the disk for general smooth elastic tension on the boundary. This is joint work with Eduardo Garcia-Juarez.

In the second part of the talk, I will present a new, recent result, in which we address the major open problem of proving the global asymptotic stability of the sphere in the 3D setting. This is joint work with Eduardo Garcia-Juarez and Yoichiro Mori.