Well-posedness and global behavior of the Peskin problem
I will discuss the behavior of an immersed elastic filament in a static Stokes flow. This problem arises in the study of microorganism and the design of microfluidic devices, among other places. The equation modeling this problem is a nonlocal integrodifferential equation with some similarities to the classical Muskat problem. I will describe local and global well-posedness results and give some qualitative features of solutions. Finally, I will make some connections between our problem and the immersed boundary method, developed by Peskin in the 70's. This is joint work with Analise Rodenberg and Yoichiro Mori.