Abstract
We introduce and study the tangential Peskin problem in 2D, which is a scalar drift-diffusion equation with a nonlocal drift. It is derived with a new Eulerian perspective from a special setting of the 2D Peskin problem where an infinitely long and straight 1D elastic string deforms tangentially in the Stokes flow induced by itself in the plane. For initial datum in the energy class satisfying natural weak assumptions, we prove existence of its global solutions. This is considered as a super-critical problem in the existing analysis of the Peskin problem based on Lagrangian formulations. Regularity and long-time behaviour of the constructed solution is established. Uniqueness of the solution is proved under additional assumptions.
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