报告题目：Smooth transonic flows with nonzero vorticity to a quasi two dimensional steady Euler flow model

报 告 人：翁上昆

工作单位：武汉大学

报告时间：2023-11-29（周三） 14:40—17:40

腾讯会议：794 364 7383

报告摘要：This talk concerns studies on smooth transonic flows with nonzero vorticity in De Laval nozzles for a quasi two dimensional steady Euler flow model which is a generalization of the classical quasi one dimensional model. First, the existence and uniqueness of smooth transonic flows to the quasi one-dimensional model, which start from a subsonic state at the entrance and accelerate to reach a sonic state at the throat and then become supersonic are proved by a reduction of degeneracy of the velocity near the sonic point and the implicit function theorem. These flows can have positive or zero acceleration at their sonic points and the degeneracy types near the sonic point are classified precisely. We then establish the structural stability of the smooth one dimensional transonic flow with positive acceleration at the sonic point for the quasi two dimensional steady Euler flow model under small perturbations of suitable boundary conditions, which yields the existence and uniqueness of a class of smooth transonic flows with nonzero vorticity and positive acceleration to the quasi two dimensional model. The positive acceleration of the one dimensional transonic solutions plays an important role in searching for an appropriate multiplier for the linearized second order mixed type equations. A deformation-curl decomposition for the quasi two dimensional model is utilized to deal with the transonic flows with nonzero vorticity. This is a joint work with Prof. Zhouping Xin.

报告人简介：翁上昆，武汉大学数学与统计学院教授，博士生导师。2007年本科毕业上海交通大学数学系，2012年获香港中文大学数学哲学博士学位。主要从事流体力学非线性偏微分方程研究，在亚音速管道流，高维跨音速激波、光滑跨音速流、不可压Hall磁流体方程光滑解奇性爆破、定常不可压Navier-Stokes方程强解的衰减性等方面做过一系列的工作。主持和参与国家自然科学基金3项。2013年获新世界数学奖博士论文银奖，曾入选国家海外高层次人才计划青年项目。

报告题目：Vanishing viscosity limits for the free boundary problem of compressible viscoelastic flows with or without surface tension

报 告 人：梅 钰

工作单位：西北工业大学

报告时间：2023-11-29（周三） 18:00-21:00

腾讯会议：794 364 7383

报告摘要：In this talk, we will present some results on the vanishing viscosity limits for compressible viscoelastic flows with free boundary. We prove the uniform regularity of classical solutions to compressible isentropic viscoelastic fluid equations with or without surface tension in Sobolev spaces and justify the corresponding vanishing viscosity limits. The proof relies on the inherent structure of the elastic term and the results indicate the boundary layer does not appear in the free boundary problem of compressible viscoelastic flows.

报告人简介：梅钰，西北工业大学，教授。2016年博士毕业于香港中文大学。2016年至2020年分别在澳大利亚昆士兰大学和意大利格兰萨索科学研究所从事博士后研究。主要从事非线性偏微分方程，特别是流体动力学方程方面的研究，具体研究兴趣为可压缩Navier-Stokes 及磁流体方程组适定性，可压缩流体自由边值问题的适定性以及渐近极限，液晶流方程的适定性。研究结果发表在M3AS,CVPDE,SIMA,JDE等国际学术期刊上。

报告题目：Incompressible limit of isentropic Navier-Stokes equations with ill-prepared data in bounded domains

报 告 人：欧耀彬

工作单位：中国人民大学

报告时间：2023-11-30（周四） 8:30-11:30

腾讯会议：794 364 7383

报告摘要：In this talk, we discuss the incompressible limit of strong solutions to the isentropic compressible Navier-Stokes equations with ill-prepared initial data and slip boundary condition in a three-dimensional bounded domain. Previous results only deal with the cases of the weak solutions or the cases without solid boundary, where the uniform estimates are much easier to be shown. We propose a new weighted energy functional to establish the uniform estimates, in particular for the time derivatives and the high-order spatial derivatives. The estimates of highest order spatial derivatives of fast variables are subtle and crucial for the uniform bounds of solutions. The incompressible limit is shown by applying the Helmholtz decomposition, the weak convergence of the velocity and the strong convergence of its divergence-free component. This is a joint work with Lu Yang.

报告人简介：欧耀彬，中国人民大学教授，于2008年在香港中文大学获博士学位，曾入选教育部“新世纪优秀人才支持计划”。主要研究方向为流体力学中的偏微分方程理论，在J. Math. Pure. Appl.、SIAM J. Math. Anal.、ANIHP (C)Anal. Non.、J. Diff. Eqns.等著名杂志发表论文30余篇，主持过多项国家级项目和省部级科研项目。

报告题目：On global well posedness of the compressible Navier Stokes equations with large initial values on bounded domains

报 告 人：樊心宇

工作单位：北京应用物理与计算数学研究所

报告时间：2023-11-30（周四） 14:30-17:30

腾讯会议：794 364 7383

报告摘要：In this talk, we focus on a model introduced by Vaigent-Kazhikov which describes the motion of compressible fluid. Compared with the classical Navier-Stokes equations, the shear viscosity coefficient is a constant, while the bulk one is given by λ=ρ^β . We first establish the global existence and uniqueness of the smooth solution on unit disc under Navier-slip boundary conditions. Then, we utilize the conformal mapping together with the pull back Green function  to  extend  the  well  posedness  result  to  general  bounded  smooth  simply  connected  domains.

报告人简介：樊心宇，助理研究员，博士毕业于中国科学院数学与系统科学研究院，导师：李竞研究员。目前为北京应用物理与计算数学研究所课题博士后，合作导师：江松院士 琚强昌研究员。