Well-Posedness of the 3D Peskin Problem
Well-Posedness of the 3D Peskin Problem
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Robert Strain, University of Pennsylvania
*Please note the time and location for this talk*
This talk introduces the 3D Peskin problem: a two-dimensional elastic membrane immersed in a three-dimensional 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 well-posed in low-regularity H枚lder spaces. Moreover, we prove that the elastic membrane becomes smooth instantly in time.听This is a joint work with Eduardo Garc铆a-Ju谩rez, Po-Chun Kuo, and Yoichiro Mori.