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.