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Open Inextensible Filaments in Planar Stokes Flow: Well-Posedness, Endpoint Asymptotics, and Straightening
We study an inextensible open filament with free ends in a planar Stokes fluid. The system reduces to a third-order nonlocal curvature equation coupled to an elliptic equation for the tension. We prove local well-posedness for nearly critical initial data in supported Sobolev spaces $\widetilde H^s$
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