| Abstract: |
| In this talk, we present stability results for an elastic string with bending and stretching energy immersed in a 2-D Stokes flow. We introduce the curve`s tangent angle function and the stretching function to describe the different deformations of the elastic string. These two functions are defined on the arc-length coordinate and the material coordinate respectively. Reformulating the problem into a parabolic system via the fundamental solution of the Stokes equation, we establish local well-posedness in Sobolev space under non-self-intersecting and well-stretched initial configurations. For initial configurations close to an evenly parametrized circle, we prove that the solution can be extended globally and the global solution will converge exponentially to the equilibrium state. |
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