丘成桐中心几何与方程组周末讨论班
SEU Yau Center Geometry and PDE Weekend Seminar
为活跃中心学术氛围，促进成员间的学术交流并激发合作，丘成桐中心几何与方程组从2022年9月末开始定期组织周末讨论班。周末研讨班面向几何与方程组和全体中心成员、数学学院研究生及感兴趣的校内外师生。
2022年12月31日，几何与方程组第九次周末讨论班将由德国雷根斯堡大学刘亚东主讲，报告信息如下。
Title: On a diffuse interface model for incompressible viscoelastic two-phase flows
Speaker: Yadong Liu（刘亚东）
Affiliation：Universität Regensburg（德国雷根斯堡大学）
Time: 10:00-11:00, December 31st (Sat.), 2022 (GMT+8)
Venue: 腾讯会议/VooV Meeting (ID: 326-304-294)
入会链接：https://meeting.tencent.com/dm/nLajgN26LoVt
Abstract:
This talk concerns a diffuse interface model for the flow of two incompressible viscoelastic fluids in a bounded domain. More specifically, the fluids are assumed to be macroscopically immiscible, but with a small transition region, where the two components are partially mixed. Considering the elasticity of both components, one ends up with a coupled Oldroyd-B/Cahn—Hilliard type system, which describes the behavior of two-phase viscoelastic fluids. We prove the existence of weak solutions to the system in two dimensions for general (unmatched) mass densities, variable viscosities, different shear moduli, and a class of physically relevant and singular free energy densities that guarantee that the order parameter stays in the physically reasonable interval. The proof relies on a combination of a novel regularization of the original system and a new hybrid implicit time discretization for the regularized system together with the analysis of an Oldroyd-B type equation. This talk is based on joint work with Dennis Trautwein (Regensburg).
Speaker:
Yadong Liu is currently a third-year doctoral student at the University of Regensburg, under the supervision of Prof. Dr. Helmut Abels (Regensburg) and PD. Dr. Maria Neuss-Radu (FAU Erlangen-Nürnberg). Before that, he received M.Sc and B.Sc. degrees from Nanjing University of Information Science and Technology under the supervision of Prof Wenjun Liu. His research mainly focuses on the analysis of nonlinear PDEs about fluid dynamics, including free boundary problems, fluid-structure interaction problems, viscoelastic flow, etc.