Analysis of the Dynamics of Immersed Elastic Filaments in Stokes Flow

Abstract: We consider the problem of an elastic filament immersed in a 2D or 3D Stokes fluid. We first discuss the analysis of an immersed filament problem in a 2D Stokes fluid (the Peskin problem). We prove well-posedness and immediate regularization of the elastic filament configuration and discuss criteria for global existence. We will then discuss the immersed filament problem in a 3D Stokes fluid (the Slender Body problem). Here, it has not even been clear what the appropriate mathematical formulation of the problem should be. We propose a mathematical formulation for the Slender Body problem and discuss well-posedness for the stationary version of this problem. Furthermore, we prove that the Slender Body approximation, introduced by Keller and Rubinow in the 1980's and used widely in computation, provides an approximation to the Slender Body problem.

mathematical physicsanalysis of PDEsclassical analysis and ODEsdynamical systemsnumerical analysis

Audience: researchers in the topic

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