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Analysis Seminar

Thursday, April 11, 2024 - 3:30pm

Po-Chun Kuo

University of Pennsylvania


University of Pennsylvania

DRL 4E19

We study the dynamics of 2D inextensible immersed interface problems. These problems consider a closed and inextensible filament with no thinckness immersed in 2D Stokes flow. Through the boundary integral method, we reformulate the problem into two contour equations, an evolution equation and a tension determination equation. The tension determination equation is for determining the tension on the filament that ensures the filament inextensibility. We first study the well-posedness and the regularity of the generalized tension determination problem in Holder spaces. Next, we use a suitable time-weighted Holder space to study the well-posedness and the regularity of the dynamic problem.