会议时间：2022年3月12日下午14:50 - 17:20

腾讯会议：484 280 730 会议密码：220312

特邀专家(按姓氏字母排序):

丁时进 (华南师范大学)

琚强昌 (北京应用物理与计算数学研究所)

温焕尧 (华南理工大学)

姚 磊 (西北大学)

原保全 (河南理工大学)

朱长江 (华南理工大学)

主办单位：广东技术师范大学大象研究院

会议资助：国家自然科学基金、广东技术师范大学科研启动经费

组织委员会：温焕尧 （华南理工大学）

姚 磊 （西北大学）

赵新花 （广东技术师范大学）

联系人: 赵新花 (电子邮箱：xhzhao@gpnu.edu.cn )

会议议程

报告题目和摘要

Global well-posedness of the Incompressible inhomogeneous generalized MHD Equations

原保全 （河南理工大学）

摘要: In this talk I will talk the Cauchy problem of the multi-dimensional incompressible inhomogeneous generalized magnetohydrodynamic equations with fractional dissipation. It is shown that when $\alpha+\beta=1+\frac{n}{2}$ satisfying $1\le \beta\le \alpha\le\min \{\frac{3\beta}{2},\frac{n}{2},1+\frac{n}{4}\}$ and $\frac{n}{4}<\alpha$ for $n\geq2$, then the incompressible inhomogeneous MHD equations has a unique global strong solution for the initial data in some Sobolev spaces. The global strong solutions to the 2D incompressible inhomogeneous magnetohydrodynamic equations with partial diffusion will be discussed.

A Singular limit of shallow water dynamics with fast variable coefficients

琚强昌 （北京应用物理与计算数学研究所）

摘要: For flows in the equatorial zone, one has to take into account the variations of the Coriolis force since the Coriolis force totally degenerates at the equator. This makes the problem more intricate as one is faced with a singular limit problem with variable coefficient. We study the singular limit of the equatorial shallow-water system which describes the motion of the atmosphere/ocean in the equatorial zone. Based on the convergence result of Durtrifoy, Majda and Schochet [Comm. Pure Appl. Math(2009)], we further obtain the convergence rate estimates of the solutions. This is a recent joint work with Prof. Jiang, Song and Prof. Xu, Xin.

Hydrodynamic limit for inhomogeneous incompressible Navier-Stokes-Vlasov-Fokker-Planck/Navier-Stokes-Vlasov equations

姚磊 （西北大学）

摘要: We study the hydrodynamic limit of the weak solutions to inhomogeneous incompressible Navier-Stokes-Vlasov-Fokker-Planck equations in a two or three dimensional bounded domain. The proof relies on the relative entropy argument to obtain the strong convergences of the macroscopic density of the particles and fluid velocity, which extends the works of Goudon-Jabin-Vasseur[Indiana Univ. Math. J., 53(2004)] and Mellet-Vasseur [Comm. Math. Phys.,281(2008)] to inhomogeneous incompressible Navier-Stokes-Vlasov-Fokker-Planck equations. At last, we give a recent progress about the hydrodynamic limit of the weak solutions to inhomogeneous incompressible Navier-Stokes-Vlasov equations in three dimensional periodic domain, under the assumption that the initial data is small in some sense and the initial density is bounded away from zero.

欢迎感兴趣的老师和同学参加！