Regularized Stokes Immersed Boundary Problem in Two-Dimensions: Well-Posedness, Singular Limit, and Error Estimates

Regularized Stokes Immersed Boundary Problem in Two-Dimensions: Well-Posedness, Singular Limit, and Error Estimates

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Jiajun Tong, University of California, Los Angeles

Zoom link: https://princeton.zoom.us/j/9148065146

In this talk, we discuss regularized 2-D Stokes immersed boundary problem, inspired by the numerical immersed boundary method. It describes certain regularized motion of a 1-D closed elastic string immersed in a 2-D Stokes flow. We will first discuss its global well-posedness. As the regularization parameter diminishes, we show that the string dynamics will converge to that in an un-regularized problem. Viewing the latter as a benchmark, we derive error estimates under various norms. Our rigorous results not only coincide with existing numerical observations in many aspects, but also imply a potential way of improving the (numerical) accuracy by choosing the regularization suitably.