演讲人：琚强昌,牛冬娟,窦昌胜

讲座时间：2017-03-21 14:00:00

讲座地点：信息楼257会议室

讲座内容

为交流近年来在偏微分方程领域所取得的最新研究成果，研讨相关的前沿课题，同时促进北京地区偏微分方程领域的青年学者间的合作，中国人民大学信息学院决定举办本次小型研讨会。诚邀各位老师和研究生参加！

组织者：欧耀彬

时间：2017年3月21日下午14:00-17:00

地点：信息楼257会议室

本次会议不收取会务费，费用自理。

日程安排

14:00 – 15:00 Singular limits of the symmetric hyperbolic equations

Prof. 琚强昌 （北京应用物理与计算数学研究所）

Abstract: The main results of the singular limits of the symmetric hyperbolic equations will be reviewed. Then the recent results of Alven limits for compressible MHD system will be presented.

15:00 – 16:00 On the incompressible fluids with helical symmetry

Prof. 牛冬娟（首都师范大学）

Abstract: In this talk, we study the weak solutions of the three-dimensional incompressible Euler equations with helical symmetry in the whole space when the helical swirl vanishes. Specifically, we establish the global existence of weak solutions when the initial vorticity lies in L1 ∩ Lp with p > 1. Our result extends the previous work of Bronze, M. Lopes and H. Lopes, where the initial vorticity is compactly supported and belongs to Lp with p >4/3. The key ingredient in this talk involves the explicit analysis of Biot–Savart law with helical symmetry in domain R2 × [−π, π] via the theories of singular integral operators and second order elliptic equations. It is a joint work with Quansen Jiu and Jun Li.

16:00—17:00 Well-posedness and incompressible limit of solutions to compressible Navier-Stokes equations with degenerate viscosity coefficients

Prof. 窦昌胜（首都经济贸易大学）

Abstract: In this talk, I will first present a recent result on the incompressible limit of compressible Navier-Stokes equations with non-constant viscosity and heat conducting coefficients. The uniform estimates in the Mach number for the strong solutions are derived, provided that the initial density and temperature are close to the constant states. Consequently, the solutions of the compressible Navier-Stokes equations converge to the one of the incompressible Navier-Stokes equations, as the Mach number vanishes. Next, I state another result on the global existence of weak solutions to compressible Navier-Stokes equations with degenerate viscosity.