May8,2022
西南交通大学数学学院
四川成都
会议主题：
为加强学术交流，提高西南交通大学数学学院偏微分方程团队的科研水平，西南交通大学数学学院将于2022年5月8日以腾讯会议的方式举办“偏微分方程小型研讨会”。本次学术会议将以学术报告的形式围绕偏微分方程研究展开讨论，旨在深入探讨该领域的一些最新研究成果，同时促进西南交通大学微分方程团队与国内同行专家的学术交流合作。
邀请专家（按姓氏拼音排序）
联系人：龚桂琼电话：15927280980 邮箱：gqgong@swjtu.edu.cn
彭英萍电话：18482202360 邮箱：yingpingpeng@swjtu.edu.cn
王凡 电话：13880013875 邮箱：wangf767@swjtu.edu.cn
钟华 电话：13648006537 邮箱：huazhong@swjtu.edu.cn
会议方式： 腾讯会议（在线会议）
会议ID：230-753-975
详细信息如下：
会议主题：偏微分方程小型研讨会
会议时间：2022/05/08 08:30-17:30 (GMT+08:00)中国标准时间-香港
点击链接入会，或添加至会议列表：
https://meeting.tencent.com/dm/f2O9q2pqsfw5
#腾讯会议：230-753-975
组织单位：
西南交通大学数学学院
数学学院数学系
数学中心
偏微分方程小型研讨会 会议日程表
Oblique injection of incompressible ideal fluid from a slot into a free stream
杜力力教授
四川大学
Abstract:
In this talk, we will discuss a two-phase fluid free boundary problem in a slot-film cooling. We will give two well-posedness results on the existence and uniqueness of the incompressible inviscid two-phase fluid with a jump relation on free interface. The problem formulates the oblique injection of an incompressible ideal fluid from a slot into a free stream. From the mathematical point of view, this work is motivated by the pioneer work in1986 by A. Friedman, in which some well-posedness results are obtained in some special case.Furthermore, A. Friedman proposed an open problem on the existence and uniqueness of the injection flow problem for more general case. The main results in this talk solve the open problem and establish the well-posedness results on the physical problem. This is a joint work with Jianfeng Cheng.
Quartic dissipation of Landau equation
段仁军教授
香港中文大学
Abstract：
For perturbation solutions to the Landau equation near Maxwellians, we introducea weighted energy functional whose dissipation rate is quartic and we use it for treating the large-velocity growth in the nonlinear estimates due to degeneration of the linearized collision operators for soft potentials. As an application, I will talk about the stability of contact waves for the Landau equation in the Coulomb case.
Local well-posedness for two-phase fluid motion in Oberbeck-Boussinesq approximation
郝成春教授
中国科学院数学与系统科学研究院
Abstract：
Low Mach number limit of Navier-Stokese quations with large temperature variations in bounded domains
琚强昌教授
北京应用物理与计算数学研究所
Abstract：
The low Mach number limit of full compressible Navier-Stokes equations with large temperature variations is verified rigorously in a three-dimensional bounded domain.Weighted uniform estimates of the solutions are derived delicately in a time interval which is independent of the Mach number,in particular,for the high-order derivatives,when the initial data are well prepared only in the sense of L2-norm.The effects of large temperature variations and solid boundaries create some essential difficulties in showing the uniform estimates.This is a recent joint work with Prof. Ou, Yaobin from Renmin University.
Localization for general Helmholtz
李栋教授
南方科技大学
Abstract：
We will discuss a novel and general symbolic framework for the Helmholtz equivalence problem.
Lipschitz continuity of steady subsonic-sonic potential flows
王春朋教授
吉林大学
Abstract：
In this talk, I introduce the regularity of steady subsonic-sonic potential flows, which are governedby a quasilinear degenerate elliptic equation. By a Moser iteration, it is shown that a two-dimensional subsonic-sonic flow is locally Lipschitz continuous. As to the boundary regularity, it is proved that the flow is also Lipschitz continuous on a given smooth streamline.
Time-asymptotic stability of viscous shock and rarefaction waves to the compressible Navier-Stokes equations
王益教授
中国科学院数学与系统科学研究院
Abstract：
The talk is concerned with our recent developments on the time-asymptotic stability of the composite wave of viscous shock and rarefaction to the one-dimensional compressible isentropic Navier-Stokes equations and the planar viscous shock wave to the three-dimensional Navier-Stokes equations. The main points in our proofs are based on the suitable choosing the time-dependent shift functions and the weight functions for the relative entropy estimates and the delicate using the Poincare-type inequality (new in 3D case) to overcome the difficulties due to the compressibility of the viscous shock.
On some reaction-diffusion models with density-dependent diffusion
王治安教授
香港理工大学
Abstract：
In this talk, I will discuss several mathematical models with density-dependent motility describing numerous biological processes, like chemotaxis, bacterial pattern formation, predator-prey models, and introduce some theoretical and numerical results obtained for them.
