In this talk, we will first review the Peskin problem in 2-D, and then we introduce the so-called tangential Peskin problem with a novel Eulerian perspective. For arbitrary non-negative initial data in the energy class satisfying some natural conditions, we prove existence of its global weak solution. This is considered as a super-critical problem in the existing studies with Lagrangian perspectives. Regularity and long-time behavior of the constructed solution is established. Uniqueness is proved under additional assumptions.

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