中科院数学与系统科学研究院

数学研究所

中科院华罗庚数学重点实验室

华罗庚青年数学论坛

综合报告

报告人：乐鹏宇 博士（BIMSA，北京雁栖湖应用数学研究院）

题  目：Null hypersurfaces and the Penrose inequality for a perturbed Schwarzschild black hole

时  间：2021.10.15（星期五），09:00-10:00

地  点：数学院南楼N204室

摘  要：The Penrose inequality conjectures a simple relation between the total mass of spacetime and the area of a black hole inside it. Penrose's original argument supporting this inequality relates it to some most challenging problems in GR, like the final state of the evolution of black holes and naked singularities (the weak cosmic censorship conjecture). A major breakthrough was achieved independently by Huisken, Ilmanen and by Bray, proving the Riemannian Penrose inequality. Besides the Riemannian case, there is another important case of the inequality on null hypersurfaces which is still open. The speaker will present his work confirming the null Penrose inequality for a perturbed Schwarzschild black hole. A major ingredient of the work is the study on perturbations of null hypersurfaces.

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  报告人：童嘉骏 博士（北京国际数学研究中心）

题  目：Two-Dimensional Stokes Immersed Boundary Problem and its Regularizations

时  间：2021.10.22（星期五），11:00-12:00

地  点：数学院南楼N204室

摘  要：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.