Kernel-adapted Schauder estimates in critical Hölder/Besov spaces yield local and global well-posedness for the Muskat equation with surface tension and Peskin problems with nonlinear elastic tension.
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Schauder-type Estimates and Well-posedness for Nonlocal Quasilinear Evolution Equations in Fluid Dynamics
Kernel-adapted Schauder estimates in critical Hölder/Besov spaces yield local and global well-posedness for the Muskat equation with surface tension and Peskin problems with nonlinear elastic tension.