Anchored Peskin filaments evolve by a fractional Laplacian with homogeneous Dirichlet conditions, have circular-arc equilibria for broad elastic energies, and regularize instantly to C^∞.
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Global well-posedness is established for a nonlocal curve evolution of an immersed elastic filament, together with convergence to resistive force theory as the filament thickness approaches zero.
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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Anchored Peskin Problem
Anchored Peskin filaments evolve by a fractional Laplacian with homogeneous Dirichlet conditions, have circular-arc equilibria for broad elastic energies, and regularize instantly to C^∞.
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A nonlocal curve evolution for an immersed elastic filament: global existence and convergence to resistive force theory
Global well-posedness is established for a nonlocal curve evolution of an immersed elastic filament, together with convergence to resistive force theory as the filament thickness approaches zero.
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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.