Well-Posedness of Hydrodynamics on the Moving Elastic Surface |
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Authors: | Wei Wang Pingwen Zhang Zhifei Zhang |
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Institution: | 1. LMAM and School of Mathematical Science, Peking University, Beijing, 100871, China
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Abstract: | The dynamics of a membrane are that of a coupled system comprising a moving elastic surface and an incompressible membrane fluid. We will consider a reduced elastic surface model, which involves the evolution equations of the moving surface, the dynamic equations of the two-dimensional fluid, and the incompressible equation, all of which operate within a curved geometry. In this paper, we prove the local existence and uniqueness of the solution to the reduced elastic surface model by reformulating the model into a new system in the isothermal coordinates. One major difficulty is that of constructing an appropriate iterative scheme such that the limit system is consistent with the original system. |
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