题目一：Well-posedness for Incompressible NS and MHD Equations with Variable Viscosity

内容简介：In this talk, we consider the initial-boundary value problem of the incompressible MHD equations with variable viscosity and conductivity in a smooth bounded domain. We establish the global well-posedness of strong solutions in both non-vacuum and vacuum cases when the initial velocity field and magnetic field are suitably small in some sense with arbitrarily large initial density. In addition, we also get some results of the large-time behavior in both two cases. Our results generalize some previous results in some sense.

报告人：华南理工大学  李用声  教授

报告人简介：李用声教授是在华东师范大学数学系读本科、研究生，1988年获得硕士学位；1995年在华中理工大学数学系获得博士学位；1995年—1998年在北京应用物理与计算数学研究所博士后流动站做博士后；现在华南理工大学数学科学学院任教，系二级教授、博士生导师。李用声教授长期从事本科生和研究生的教学工作，一直进行非线性偏微分方程理论的学习及研究，主要研究方向为非线性发展方程和无穷维动力系统的理论及应用。主持完成和正在研究的国家自然科学基金项目5项，省自然科学基金项目1项，省优秀博士论文作者资助项目1项。在国内外重要学术刊物、论文集上发表论文70 余篇。

时  间：2017年6月13日（周二）下午3：30始

题目二：Global regularity and time decay for the 2D MHD equations with partial dissipations

内容简介：The magnetohydrodynamic (MHD) equations with only magnetic diffusion play a significant role in the study of magnetic reconnection and magnetic turbulence. In certain physical regimes and under suitable scaling the magnetic diffusion becomes partial (given by part of the Laplacian operator). Such equations are of great mathematical interest as well. There have been considerable recent developments on the fundamental issue of whether classical solutions of these partially dissipated equations remain smooth for all time. This problem remains open for the 2D MHD equations with the standard Laplacian magnetic diffusion. This talk focuses on a system of the 2D MHD equations with the kinematic dissipation given by the fractional operator (−Δ)_α and the magnetic diffusion by partial Laplacian. We are able to show that this system with any α > 0 always possesses a unique global smooth solution when the initial data is sufficiently smooth. In addition, we make a detailed study on the large-time behavior of these smooth solutions and obtain optimal large-time decay rates. Since the magnetic diffusion is only partial here, some classical tools such as the maximal regularity property for the 2D heat operator can no longer be applied. A key observation on the structure of the MHD equations allows us to get around the difficulties due to the lack of full Laplacian magnetic diffusion.

报告人：深圳大学  董柏青  教授

报告人简介：深圳大学教授、博士生导师。分别于2004年6月和2007年6月在华中科技大学和南开大学获硕士和博士学位，同年7月到安徽大学工作。现为美国《Mathematical Review》评论员。近十年来一直致力于流体动力学方程研究，在描述复杂流动的非线性偏微分方程解的存在唯一性，正则性，衰减性，稳定性和动力学性态等方面做了一些较好的工作。董教授先后在Nonlinearity，J.Differential Equations，Discrete Contin. Dyn. Syst， J. Math. Phys等重要国际期刊上发表SCI收录论文40余篇，研究工作被国内外同行在主流期刊上SCI他引100余次，曾主持多项国家自然科学基金项目。

时  间：2017年6月13日（周二）下午4：30始

地  点：南海楼224室

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2017年6月9日