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.
Garc´ ıa-Ju´ arez and S
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Establishes a solution theory for the slender body free boundary problem of an inextensible closed elastic filament in Stokes flow via the Neumann-to-Dirichlet map and tension enforcement.
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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.
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The slender body free boundary problem
Establishes a solution theory for the slender body free boundary problem of an inextensible closed elastic filament in Stokes flow via the Neumann-to-Dirichlet map and tension enforcement.