Global Well-Posedness of the 2-D Peskin Problem under Geometric Conditions
Prof. Jiajun Tong
2023-06-21 10:30-11:30
MCM110
Speaker: Prof. Jiajun Tong (BICMR)Time: 10:30-11:30 June 21, 2023 (Wednesday)
Place: MCM110
Title: Global Well-Posedness of the 2-D Peskin Problem under Geometric Conditions
Abstract: The 2-D Peskin problem describes coupled motion of a 1-D closed elastic string and the ambient Stokes flow in the plane. In existing works, its global well-posedness has been proved when the initial string configuration is close to an equilibrium. More precisely, initial shape of the string needs to be almost circular, and the string is almost evenly-stretched. In this talk, we present some recent progress on pursuing global solutions for a wider class of initial datum. We start from a 1-D simplified model, and show that global solutions exist for rather arbitrary initial datum in the energy class. Then we return to the original 2-D Peskin problem, and show that certain geometric quantities of the string satisfy extremum principles and decay estimates. As a result, global well-posedness can be proved for initial datum satisfying a medium-size geometric condition on the string shape, while no assumption on the size of stretching is needed. This talk is based on a joint work with Dongyi Wei.
