Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars
| | Speaker: | 童嘉骏 博士，北京国际数学研究中心
| | Inviter: | | Title:
| Two-Dimensional Stokes Immersed Boundary Problem and its Regularizations | Time & Venue:
| 2021.10.22 11:00-12:00 南楼N204室 | Abstract:
| In this talk, we first consider 2-D Stokes immersed boundary problem. It models a 1-D closed elastic string immersed and moving in a 2-D Stokes flow, which features an autonomously moving boundary and singular forcing supported on it. We will discuss results on well-posedness of the string motion (joint work with Fanghua Lin). In the second part of the talk, we introduce a regularized version of the problem inspired by the closely-related numerical immersed boundary method, where a regularized delta-function is used to mollify the singular forcing and the flow field. After proving global well-posedness of the regularized string motion, we will show that, as the regularization diminishes, the string dynamics converges to that in the un-regularized case under certain assumptions. Viewing the latter as a benchmark, we derive error estimates under various norms. Our rigorous results coincide with existing numerical observations in many aspects.
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