WellPosedness of the 3D Peskin Problem
WellPosedness of the 3D Peskin Problem

Robert Strain, University of Pennsylvania
Fine Hall 601
*Please note the time and location for this talk*
This talk introduces the 3D Peskin problem: a twodimensional elastic membrane immersed in a threedimensional steady Stokes flow. We obtain the equations that model this free boundary problem and show that these equations admit a boundary integral reduction, providing an evolution equation for the elastic interface. We consider general nonlinear elastic laws, i.e., the fully nonlinear 3D Peskin problem, and we prove that the problem is wellposed in lowregularity Hölder spaces. Moreover, we prove that the elastic membrane becomes smooth instantly in time. This is a joint work with Eduardo GarcíaJuárez, PoChun Kuo, and Yoichiro Mori.