报告题目：Relative entropy, weak-strong uniqueness, and conditional regularity for a compressible Oldroyd-B model.

报告人：吕勇副教授（南京大学）

报告时间：2021年11月26日14：00-17：00

报告地点：数学与统计学院4号楼302室/ID: 788-436-987

报告摘要：

We study the compressible Oldroyd-B model derived in [J. W. Barrett, Y. Lu and E. E. Süli, Commun. Math. Sci. 15 (2017), no. 5, 1265–1323; MR3668885]. The existence of global-in-time finite-energy weak solutions was shown previously in a two-dimensional setting. In this paper, the authors first state a local well-posedness result for this compressible Oldroyd-B model. In the two-dimensional setting, they give a (refined) blow-up criterion involving only the upper bound of the fluid density. Then they show that if the initial fluid density and polymer number density admit a positive lower bound, the weak solution coincides with the strong one as long as the latter exists. Moreover, if the fluid density of a weak solution issuing from regular initial data admits a finite upper bound, this weak solution is indeed a strong one; this can be seen as a corollary of the refined blow-up criterion and the weak-strong uniqueness（分三个学时讲）.

报告人简介：

吕勇，南京大学副教授，博士生导师，国家高层次青年人才入选者。本科毕业于中国科技大学数学系，在法国巴黎七大取得硕士和博士学位，之后在布拉格查理大学从事博士后研究。吕勇的研究领域是非线性几何光学以及流体力学中偏微分方程的数学分析，主要研究成果发表在Archive for Rational Mechanics and Analysis, Mémoires de la Société Mathématique de France，Calculus of Variations and Partial Differential Equations，SIAM: Journal on Mathematical Analysis, ESAIM: Control, Optimisation and Calculus of Variations, Journal of Differential Equations等国际著名SCI数学期刊上。