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m4ª 6401

8:309:00

���§þ°�Ï�ÆGlobal Existence of Large Solutions to Conservation Laws withNonlocal Dissipation-Type Terms

6401

"±²9:009:30

Û7§�l¢½�ÆOn Fluid Interface Problems

6401

9:3010:00

4yǧ�²�ÆMean curvature flow with a constant forceing term.

6401

10:00-10:30 � �

10:3011:00

¶�?§uH���ÆStability analysis for the incompressible Navier-Stokes equa-tions with Navier boundary conditions

6401

¯��11:0011:30

4�J§uHnó�ÆSome studies on stochastic KPP and Novikov equations

6401

11:3012:00

o¿§¥I�Æ�êÆ�XÚ�ÆïÄ�Large-Time Behavior of Solutions to 1D Compressible Navier-Stokes System in Unbounded Domains with Large Data

6401

12:00-14:00 Ì ê£? � U ,¤

u¥���Æ Ä3“ �©�§9ÙA^”ÆâØ� 17�

Æâ�wSüL

FÏ: 12 � 17 F

ÌR �m �w<, K8 /:

14:0014:30

Õ§�l¢½�ÆMeasure valued solutions to kinetic equations

6401

îäÜ14:3015:00

§§f��ÆHeat flow for Dirichlet-to-Neumann operator with criticalgrowth

6401

15:0015:30

��S§¥ì�Æ{zEricksen¨Leslie�¬�.eZ¯K�ïÄ

6401

15:30-16:00 � �

16:0016:30

��¯§¥I�Æ�êÆ�XÚ�ÆïÄ�Isentropic compressible Euler system with source terms

6401

Á�ô16:3017:00

Ë�ܧÄÑ���ÆA Note on lifespan of SQG

6401

17:0017:30

Hýu§Ü��Æ'u6NåÆ�§¥eZêƯK�ïÄ

6401

18:00-20:00 � �£< Ù I S Ë A¤

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9:0011:30 Æ â ? Ø 6401

14:0014:30

�â§�®ó��ÆBoundary Layer Problem and Zero Viscosity-Diffusion Vanish-ing Limit of the Incompressible Magnetohydrodynamic Systemwith Dirichlet Boundary Conditions

6401

14:3015:00

o°ù§ÄÑ���ÆNon-existence of finite energy solution to Compressible Navier-Stokes equations

6401

u¥���Æ Ä3“ �©�§9ÙA^”ÆâØ� 19�

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Stability analysis for the incompressible Navier-Stokes

equations with Navier boundary conditions

¶�?§uH���Æ

In this talk§we discuss the stability and instability of trivial steady state to

the incompressible Navier-Stokes equations £with constant density¤in a two di-

mensional slab domain with Navier boundary conditions. A sharp critical viscosity

to distinquish the stability from the instability is exactly expressed in terms of the

coeffcients in the Navier boundary conditions. The linear and the nonlinear stability

and instability are analyzed. The decay estimates are also given. This is a joint work

with Quanrong Li and Zhouping Xin.

'u6NåÆ�§¥eZêƯK�ïÄ

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·�Ì�ïÄ�Ø N-S�§£Úî6NÚ�Úî6N¤)�·½59��

m1�"äN¯K�9gd>.�$ħÊ5Xê�6u�Ýڧݱ9Å�­½

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Isentropic compressible Euler system with source terms

��¯§¥I�Æ�êÆ�XÚ�ÆïÄ�

In this talk, we develop a new technique to prove the global existene of entropy

solutions to an inhomogeneous isentropic compressible Euler equations through the

compensated compactness and vanishing viscosity method.

110� Ä3“ �©�§9ÙA^”ÆâØ� u¥���Æ

A Note on lifespan of SQG

Ë�ܧÄÑ���Æ

In this talk, we consider the active scalar equation:

ωt + u · ∇ω = 0, x ∈ R2, t > 0,

u = K ∗ ω,

with K(x) = x⊥

|x|2+2α , 0 ≤ α ≤ 12. When α = 0, it is the two-dimensional Euler

equations. When α = 12, it corresponds to SQG. We will prove that if the existence

interval of the smooth solution to SQG is [0, T ], then when α < 12

the existence

interval of the active scalar equation will keep on [0, T ].

Non-existence of finite energy solution to Compressible

Navier-Stokes equations

o°ù§ÄÑ���Æ

It is an open problem to show the well-posedness of classical solution to compress-

ible Navier-Stokes equations with the density possibly containing vacuum, although

the same problem has been proved by Nash and Serrin in energy space in 1960s when

the vaccum is excluded. In this talk, we shall prove that there does not exit any

classical solution with density being compact supported to the Cauchy problem for

one-dimensional compressible Navier-Stokes equaions in energy space so long as the

initial data satisfy some properties.

Large-Time Behavior of Solutions to 1D Compressible

Navier-Stokes System in Unbounded Domains with Large

Data

o¿§¥I�Æ�êÆ�XÚ�ÆïÄ�

We study the large-time behavior of solutions to the initial and initial boundary

value problems with large initial data for the compressible Navier-Stokes system

describing the one-dimensional motion of a viscous heat-conducting perfect polytropic

gas in unbounded domains. The temperature is proved to be bounded from below and

u¥���Æ Ä3“ �©�§9ÙA^”ÆâØ� 111�

above independently of both time and space. Moreover, it is shown that the global

solution is asymptotically stable as time tends to infinity. Note that the initial data

can be arbitrarily large. This result is proved by using elementary energy methods.

Some studies on stochastic KPP and Novikov equations

4�J§uHnó�Æ

In this talk, some studies on stochastic KPP and Novikov equations will be

introduced."

Mean curvature flow with a constant forceing term.

4yǧ�²�Æ

�½"

On Fluid Interface Problems

Û7§�l¢½�Æ

In this talk, I will survey some results on fluid interface problems.

Heat flow for Dirichlet-to-Neumann operator with critical

growth

§§f��Æ

In this article, we study the heat flow equation for Dirichlet-to-Neumann op-

erator with critical growth. By assuming that the initial value is lower-energy, we

obtain the existence, blowup and regularity. On the other hand, a concentration

phenomenon of the solution when the time goes to infinity is proved.

112� Ä3“ �©�§9ÙA^”ÆâØ� u¥���Æ

Boundary Layer Problem and Zero Viscosity-Diffusion

Vanishing Limit of the Incompressible

Magnetohydrodynamic System with Dirichlet Boundary

Conditions

�â§�®ó��Æ

In this paper, we study the boundary layer problem, zero viscosity-diffusion van-

ishing limit and zero magnetic diffusion vanishing limit of the initial boundary value

problem for the incompressible viscous and diffusive magnetohydrodynamic(MHD)

system with Dirichlet boundary conditions. The main difficulties overcome here are

to deal with the effects of the the difference between the viscosity and diffusion

coefficient on the error estimates and to control the boundary layer resulted by the

Dirichlet boundary condition for the velocity and magnetic field. Firstly, we establish

the result on the stability of the Prandtl boundary layer of MHD system with a class

of special initial data and prove rigorously the solution of incompressible viscous and

diffusive MHD system converges to the sum of the solution to the ideal inviscid MHD

system and the approximating solution to Prandtl boundary layer equation by using

the elaborate energy methods and the special structure of the solution to inviscid

MHD system, which yields that there exists the cancelation between the boundary

layer of the velocity and the one of the magnetic field. Next, we obtain the stability

result on the boundary layer for the magnetic field and zero magnetic diffusion limit

of viscous and diffusive MHD system with the general initial data when the mag-

netic diffusion coefficient goes to zero. Finally, for general initial data, we consider

the boundary layer problem of the incompressible viscous and diffusive MHD system

with the different horizontal and vertical viscosities and magnetic diffusions, when

they go to zero with the different speeds. We prove rigorously the convergence to the

ideal inviscid MHD system and the anisotropic inviscid MHD system from the in-

compressible viscous and diffusion MHD system by constructing the exact boundary

layers and using the elaborate energy methods. We also mention that these results

obtained here should be the first rigorous ones on the stability of Prandtl boundary

layer for the incompressible viscous and diffusion MHD system with no-slip charac-

teristic boundary condition.

u¥���Æ Ä3“ �©�§9ÙA^”ÆâØ� 113�

Global Existence of Large Solutions to Conservation Laws

with Nonlocal Dissipation-Type Terms

���§þ°�Ï�Æ

In this talk§we are concerned with the Cauchy problem of a scalar conservation

law with a nonlocal dissipation term. By the Green function and nonlinear maximum

principle method, global classical solution and its long-time behavior are established

for arbitrary large initial data.

Measure valued solutions to kinetic equations

Õ§�l¢½�Æ

The measure valued solutions to the spatially homogeneous Boltzmann equation

has been well studied, but how about spatially inhomogeneous equation?

{zEricksen¨Leslie�¬�.eZ¯K�ïÄ

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2 ¶�? uH���Æ �Ç dingsj@scnu.edu.cn

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4 Hýu Ü��Æ �Ç zhguo@nwu.edu.cn

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18 /¯ u¥���Æ B�Ç lantang@mail.ccnu.edu.cn

19 �â �®ó��Æ �Ç wangshu@bjut.edu.cn

20 ¯�� wÅ�Æ �Ç quchangzheng@nbu.edu.cn

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25 ��S ¥ì�Æ �Ç mcsyao@mail.sysu.edu.cn

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27 Á�ô uHnó�Æ �Ç machjzhu@scut.edu.cn,

cjzhu@mail.ccnu.edu.cn

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