会议时间：北京时间2021年12月18日19日
会议地点：腾讯会议33369271375
邀请专家：
桂贵龙 （湘潭大学、西北大学）
黄景炽（中山大学）
李岩岩（罗格斯大学）

郝成春（中科院数学所）
李维喜（武汉大学）
吕勇（南京大学）

牛冬娟（首都师范大学）

潜陈印（浙江师范大学）

孙永忠（南京大学）
王文栋（大连理工大学）
张挺（浙江大学）

王飞（上海交通大学）
张平（中科院数学所、国科大）
赵威任（纽约大学）

组委会：刘彦麟 熊金钢 许孝精 薛留堂
资助：“双一流”团队项目
会议日程
2021年12月18日 周六

时间

题目

报告人

主持人

8:509:00

开幕式：胡维副院长致辞

刘彦麟

9:009:50

Anisotropic CaffarelliKohnNirenberg type inequalities

李岩岩
罗格斯大学

9:5010:40

Enhanced dissipation for the third component of 3D anisotropic NavierStokes equations

张平
中科院数学所、国科大

许孝精

10:5011:40

Asymptotic Stability of Boussinesq Equations without Thermal Conduction

孙永忠
南京大学

午 休

14:0014:50

Lagrangian approach to global wellposedness of the viscous surface wave equations

桂贵龙
湘潭大学、西北大学

许孝精

14:5015:40

Global weak solutions to a 2D compressible nonresistivity MHD

张挺
浙江大学

15:5016:40

Wellposedness of Linearized Incompressible Ideal MHD with Closed Free Surfaces

郝成春
中科院数学所

薛留堂

16:4017:30

Longtime behavior of large solutions with just bounded density to compressible NavierStokes equations

黄景炽
中山大学

2021年12月19日 周日

时间

题目

报告人

主持人

9:009:50

Homogenization of Poisson and Stokes equations in the whole space

吕勇
南京大学

熊金钢

9:5010:40

CaffarelliKohnNirenberg's regularity theory for the 3D NavierStokes equations: its generalization and application

王文栋
大连理工大学

10:5011:40

Gevrey wellposedness of Prandtl and MHD boundary layer equations

李维喜
武汉大学

午 休

14:0014:50

On the Euler+Prandtl expansion for the NavierStokes equations

王飞
上海交通大学

刘彦麟

14:5015:40

Enhanced dissipation for the 2D Couette flow

赵威任
纽约大学

15:5016:40

Global wellposedness for the 2D Boussinesq system with variable viscosity

牛冬娟
首都师范大学

薛留堂

16:4017:30

Global wellposedness for 3D incompressible inhomogeneous asymmetric fluids

潜陈印
浙江师范大学

报告题目和摘要
Lagrangian approach to global wellposedness of the viscous surface wave equations
桂贵龙
湘潭大学、西北大学
Abstract：In this talk, we investigate the global wellposedness of the classical viscous surface waves in the absence of surface tension effect with the reference domain being the horizontal infinite slab. The fluid dynamics are governed by the gravitydriven incompressible NavierStokes equations. Even though Lagrangian formulation is most natural to study free boundary value problems for incompressible flows, few mathematical works for global existence are based on such an approach in the absence of surface tension effect, due to breakdown of Beale's transformation. We develop a mathematical approach to establish global wellposedness based on the Lagrangian framework by analyzing suitable "good unknowns" associated with the problem, which requires no nonlinear compatibility conditions on the initial data.
Wellposedness of Linearized Incompressible Ideal MHD with Closed Free Surfaces
郝成春
中科院数学与系统科学研究院
Abstract：In this talk, I review some results of free boundary problem of incompressible ideal MHD in a bounded domain with closed free surfaces based on the joint works with Prof. T. Luo, especially the wellposedness for the linearized system. We expressed the magnetic field in terms of the velocity field and the deformation tensors in the Lagrangian coordinates, and substituted the magnetic field into the momentum equation to get an equation of the velocity in which the initial magnetic field serves only as a parameter. Then, we linearized this equation with respect to the position vector field whose time derivative was the velocity, and obtained the localintime wellposedness of the solution by using energy estimates of the tangential derivatives and the curl with the help of Lie derivatives and the smoothout approximation.
Longtime behavior of large solutions with just bounded density to compressible NavierStokes equations
黄景炽
中山大学
Abstract：In this talk, we will focus on the longtime behavior of large solutions with just bounded density (without vaccum) for compressible NaiverStokes equations. This result removes the Hölder condition of previous result.
Gevrey wellposedness of Prandtl and MHD boundary layer equations
李维喜
武汉大学
Abstract：We establish the wellposedness of the Prandtl and MHD boundary layer system in Gevrey function spaces. By observing new type of cancellation mechanism in the system for overcoming the loss derivative degeneracy, we show that the Prandtl and MHD boundary layer system are wellposed in Gevrey space without any structural assumption.
Anisotropic CaffarelliKohnNirenberg type inequalities
李岩岩
罗格斯大学
Homogenization of Poisson and Stokes equations in the whole space
吕勇
南京大学
Abstract：We consider the homogenization of the Poisson and the Stokes equations in the whole space perforated with periodically distributed small holes. The periodic homogenization in bounded domains is well understood, following the classical results of Tartar, CioranescuMurat, Allaire in 80s and 90s. In this paper, we show that these classical homogenization results in a bounded domain can be extended to the whole space R^d. Our results cover all three cases corresponding to different sizes of holes and cover all d\geq 2.
Global wellposedness for the 2D Boussinesq system with variable viscosity
牛冬娟
首都师范大学
Abstract：In this talk, we investigate the global wellposedness of 2D Boussinesq system, which has variable kinematic viscosity yet without thermal conductivity and buoyancy force, provided that the viscosity coefficientis sufficiently close to some positive constant in L∞. In addition, the decay estimate of the velocity fields is also obtained.It is a joint work with Lu Wang.
Global wellposedness for 3D incompressible inhomogeneous asymmetric fluids
潜陈印
浙江师范大学
Abstract：In this paper, we investigate the 3D inhomogeneous incompressible asymmetric fluids system with densitydependent viscosity. By the assumption of the smallness of initial velocity in the critical Besov space and the initial density in the critical Besov space and bounded away from vacuum, the local and global wellposedness of 3D inhomogeneous incompressible asymmetric fluids is obtained. By giving the different estimates for pressure, it shows the a priori estimate for the corresponding linearized equation. This not only improves the previous results for 3D inhomogeneous incompressible NavierStokes equations with densitydependent viscosity, but also obtains the new results on the micropolar system without smallness for density in critical Besov spaces.
Asymptotic Stability of Boussinesq Equations without Thermal Conduction
孙永忠
南京大学
Abstract：We consider the motion of viscous incompressible fluids under the action of gravitation/buoyancy modeled by the Boussinesq equations in the absence of thermal conduction which is a simple ellipticparabolichyperbolic coupled nonlinear system. The fluid motion is assumed to be in an infinite stripe domain in two or three dimensional space. The asymptotic stability is proved for a specific stationary solution in contrast to RayleighTaylor instability. Moreover, we also show exact decay rates of the solutions to the perturbed system with small initial dara. This is a joint work with Lihua Dong.
On the Euler+Prandtl expansion for the NavierStokes equations
王飞
上海交通大学
Abstract： We establish the validity of the Euler+Prandtl approximation for solutions of the NavierStokes equations in the half plane with Dirichlet boundary conditions, in the vanishing viscosity limit, for initial data which are analytic only near the boundary, and Sobolev smooth away from the boundary. Our proof does not require higher order correctors, and works directly by estimating an L 1 type norm for the vorticity of the error term in the expansion NavierStokes−(Euler+Prandtl). An important ingredient in the proof is the propagation of local analyticity for the Euler equation, a result of independent interest.
CaffarelliKohnNirenberg's regularity theory for the 3D NavierStokes equations: its generalization and application
王文栋
大连理工大学
Abstract：In this talk we'll recall CaffarelliKohnNirenberg's interior regularity theory and some generalized forms for the 3D NavierStokes equations. Moreover, we will show their important role in studying other properties of NavierStokes equations and some important applications for other models. This is a series of joint work with Professors Zhifei Zhang, Liqun Zhang, Di Wu, Jitao Liu, Tao Tao, Shuai Li, and others.
Enhanced dissipation for the 2D Couette flow
赵威任
纽约大学
Abstract：In this talk, I will first review some results about the enhanced dissipation for the 2D Couette flow. Then I will introduce a recent result about the nonlinear enhanced dissipation threshold in the cirtical space, where we proved the optimality of the size for the perturbations in critical space. This is a joint work with Li and Masmoudi.
Enhanced dissipation for the third component of 3D anisotropic NavierStokes equations
张平
中科院数学所、国科大
Abstract：In this talk, we study the decay rates for the global small smooth solutions to 3D anisotropic incompressible NavierStokesequations. In particular, we prove that the horizontal components of the velocity field decay like the solutions of 2D classical NavierStokes equations.While the third component of the velocity field decays as the solutions of 3D NavierStokes equations. We remark thatsuch enhanced decayrate for the third component is caused by the interplay between the divergence free condition of the velocity field and the horizontalLaplacian in the anisotropic NavierStokes equations.
Global weak solutions to a 2D compressible nonresistivity MHD
张挺
浙江大学
Abstract：In this talk, we consider a twodimensional nonresistivity MHD system describing the evolution of viscous compressible and electrically conducting fluids under the action of a vertical magnetic field, with nonmonotone pressure law and densitydepending viscosity λ =λ(ρ). Using an approximate scheme and the compactness method which Bresch and Jabin proposed in (Bresch and Jabin, 2018), we prove the global existence of weak solutions. (Based on the work with Yu Liu)