中科院数学与系统科学研究院
数学研究所
偏微分方程研讨班
报告人：琚强昌 研究员 (北京应用物理与计算数学研究所)
题 目：Singular limit for equatorial shallow water dynamics
时 间：2020.11.18（星期三）, 14:00-15:00
地 点：腾讯会议，会议号316 317 660
摘 要：We study the singular limit for equatorial shallow water equations at low Froude number forming a symmetric hyperbolic system with large variable coefficient terms. Based on the convergence result of Durtrifoy, Majda and Schochet [Comm. Pure Appl. Math(2009)], we further obtain the convergence rate estimates of the solutions. This is a recent joint work with Prof. Jiang, Song and Dr. Xu, Xin.
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报告人： 栗付才 教授 (南京大学)
题 目：Incompressible limit for the compressible Ericksen-Leslie's hyperbolic liquid crystal model
时 间：2020.11.18（星期三）, 15:00-16:00
地 点：腾讯会议，会议号316 317 660
摘 要：In this talk, I shall discuss the incompressible limit of the Ericksen-Leslie's hyperbolic liquid crystal model in compressible flow. We first derive the uniform energy estimates on the Mach number $\epsilon$ for both the compressible system and its differential system with respect to time under the uniformly in $\epsilon$ small initial data. Then, we take the limit in the compressible system to establish the global classical solution of the incompressible system. Moreover, we also obtain the convergence rates for the well-prepared initial data case. This talk is based on the joint work with L. Guo, N. Jiang, Y. Luo and S. Tang.
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报告人：麦拉苏 副教授 (内蒙古大学)
题 目：On the free boundary problem of porous media equations
时 间：2020.11.18（星期三）, 16:00-17:00
地 点：腾讯会议，会议号316 317 660
摘 要：In this talk, we will consider the of porous media equations when the initial data are continuous and compactly supported. The major feature is the parabolicity degenerate at the moving boundary. By introducing the proper weighted Sobolev space, which captures the degenerative at the moving boundary, the well-posedness of the local solution is established at first. Then, the global solution closed to the Barenblatt solution is constructed, and converges to the Barenblatt solution as time goes to infinity. Our results particularly give a positive answer of the open problem proposed by Lee and Vzquez on convexity.
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