会议时间：2021年12月4日6日（周六周一）
线上地址：腾讯会议 852 3393 4327
组织者：刘彦麟 熊金钢 许孝精 薛留堂
资助：“双一流”团队项目
2021年12月4日

时间

题目

报告人

地点

8:309:25

Uniform Bound of the Highestorder Energy of the 2D Incompressible Elastodynamics

蔡圆
复旦大学

腾讯会议：
85233934327

9:3010:25

Zeroviscosity limit of the NavierStokes equations in a thin domain

王渝西
四川大学

午 休

14:0014:55

The wellposedness of axially symmetric compressible subsonic jet impinging flow

程建峰
四川大学

腾讯会议：
85233934327

15:0015:55

Some recent works about incompressible and compressible MHD equations

朱异
华东理工大学

2021年12月5日

时间

题目

报告人

地点

14:0014:55

Liner Stability of Pipe Posieuille Flow at High Reynolds Number Regime

陈琦
中科院华罗庚中心

后主楼1220
腾讯会议：85233934327

15:0015:55

The Optimal Decay Rate of Strong Solution for the Compressible NavierStokes Equations and related models with Large Initial Data

魏正珍
北京理论物理与计算数学研究所

16:0016:55

From conservative to dissipative systems through quadratic change of time

段祥龙
首都师范大学

2021年12月6日

时间

题目

报告人

地点

14:0014:55

Remarks on wellposedness of the generalized SQG equation

于幻
北京信息科技大学

腾讯会议：85233934327

15:0015:55

Leray's flowpastobstacle problem: uniqueness and the invading domains method

任潇
复旦大学

报告题目和摘要
Uniform Bound of the Highestorder Energy of the 2D Incompressible Elastodynamics
蔡圆
复旦大学
Abstract: This talk concerns the time growth of the highestorder energy of the systems of two dimensional incompressible isotropic Hookean elastodynamics. This two dimensional systems are nonlocal quasilinear wave equations where the unknowns has slow temporal decay. By observing an inherent strong null structure, the global wellposedness of smooth solutions near equilibrium was first proved by Zhen Lei where the highestorder generalized energy may have certain growth in time. We improve the result and show that the highestorder generalized energy is uniformly bounded for all the time.
The wellposedness of axially symmetric compressible subsonic jet impinging flow
程建峰
四川大学
Abstract： This talk is concerned with the wellposedness theory of the impact of a subsonic axially symmetric jet emerging from a semiinfinitely long nozzle, onto a rigid wall. The fluid motion is described by the steady isentropic Euler system. We showed that there exists a critical value M_{cr}>0, if the given mass flux is less than M_{cr}, there exists a unique smooth subsonic axially symmetric jet issuing from the given semiinfinitely long nozzle and hitting a given uneven wall. The surface of the axially symmetric impinging jet is a free boundary, which detaches from the edge of the nozzle smoothly. It is showed that a unique suitable choice of the pressure difference between the chamber and the atmosphere guarantees the continuous fit condition of the free boundary. Moreover, the asymptotic behaviors and the decay properties of the impinging jet and the free surface in downstream were also obtained. This is a joint work with Prof. Lili Du (SCU) and Prof. Qin Zhang (CQJTU).
Liner Stability of Pipe Posieuille Flow at High Reynolds Number Regime
陈琦
中科院数学与系统科学研究院
Abstract：In this paper, we prove the linear stability of the pipe Poiseuille flow for general perturbations at high Reynolds number regime. This is a longstanding problem since the experiments of Reynolds in 1883. Our work lays a foundation for the theoretical analysis of hydrodynamic stability of pipe flow, which is one of the oldest yet unsolved problems of fundamental fluid dynamics.
From conservative to dissipative systems through quadratic change of time
段祥龙
首都师范大学
Abstract：There are many examples of dissipative systems that can be derived from conservative ones. A classical example is the heat equation (or more generally the porous medium equation) that can be derived from the Euler equations of isentropic gases. The derivation can be done in many ways. In this talk, we will focus on a very straightforward idea: just perform the quadratic change to the time variable $\theta=t^2/2$.
Leray's flowpastobstacle problem: uniqueness and the invading domains method
任潇
复旦大学
Abstract: We study the exterior problem for stationary Navier–Stokes equations in two dimensions describing a viscous incompressible fluid flowing past an obstacle. Two main results in the small Reynolds numbers regime will be presented: (i) uniqueness of the classical FinnSmith solutions (ii) justification of Leray's invading domains method proposed in 1933. In the proofs, we combine and develop the ideas of Amick (Acta Math 1988), asymptotic analysis for the Oseen system, and novel blowdown arguments. Moreover, we show two basic estimates for general stationary NavierStokes solutions based on the above methods, and discuss their applications. The talk is based on joint works with Mikhail Korobkov and Julien Guillod.
Zeroviscosity limit of the NavierStokes equations in a thin domain
王渝西
四川大学
Abstract： In this talk, we justify the limit from the NavierStokes system in a thin domain to the Hydrostatic NavierStokes/ Prandtl system for the convex initial data with Gevrey 3/2 regularity in the x variable, which is the optimal Gevrey index, and Sobolev regularity in the y regularity.
The Optimal Decay Rate of Strong Solution for the Compressible NavierStokes Equations and related models with Large Initial Data
魏正珍
北京理论物理与计算数学研究所
Abstract：In this talk, we are concerned with the optimal decay rate for large solution to the three dimensional compressible NavierStokes(CNS) equations and related models. More precisely, we established the upper and lower bounds of decay rates for the global solution of CNS equations when the initial perturbation is large and belongs to L^1(R^3)\cap H^2(R^3). In addition, these lower bounds of decay rate coincide with the upper one.
Remarks on wellposedness of the generalized SQG equation
于幻
北京信息科技大学
Abstract：In this talk, we are concerned with the Cauchy problem of the generalized surface quasigeostrophic (SQG) equation in which the velocity field is expressed as , where is an unknown function and . When, it is the twodimensional Euler equations. When, it corresponds to the inviscid SQG. We first present a new and elementary proof of the local existence and uniqueness of the classical solution via the method of the contraction mapping principle. Then, we prove stability of the (local) time of existence of smooth solutions with respect to . One implication is that the maximal time of existence, as a function of, blows up as approaches 0.
Some recent works about incompressible and compressible MHD equations
朱异
华东理工大学
Abstract: In this talk, we investigate the dissipative structure of both incompressible and compressible magnetohydrodynamic (MHD) systems. First, we focus on the 3D incompressible MHD equations with mixed partial dissipation and magnetic diffusion. Our main result assesses the global stability of perturbations near the steady solution given by a background magnetic field. Then we focus on the 2D compressible viscous and nonresistive MHD equations. We derive the global existence of small smooth solutions to this system on periodic domain.