題目一：Well-posedness for Incompressible NS and MHD Equations with Variable Viscosity
内容簡介：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.
報告人：華南理工大學 李用聲 教授
報告人簡介：李用聲教授是在華東師範大學數學系讀本科、研究生，1988年獲得碩士學位；1995年在華中理工大學數學系獲得博士學位；1995年—1998年在北京應用物理與計算數學研究所博士後流動站做博士後；現在華南理工大學數學科學學院任教，系二級教授、博士生導師。李用聲教授長期從事本科生和研究生的教學工作，一直進行非線性偏微分方程理論的學習及研究，主要研究方向為非線性發展方程和無窮維動力系統的理論及應用。主持完成和正在研究的國家自然科學基金項目5項，省自然科學基金項目1項，省優秀博士論文作者資助項目1項。在國内外重要學術刊物、論文集上發表論文70 餘篇。
時 間：2017年6月13日（周二）下午3：30始
題目二：Global regularity and time decay for the 2D MHD equations with partial dissipations
内容簡介：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.
報告人：深圳大學 董柏青 教授
報告人簡介：深圳大學教授、博士生導師。分别于2004年6月和2007年6月在華中科技大學和南開大學獲碩士和博士學位，同年7月到安徽大學工作。現為美國《Mathematical Review》評論員。近十年來一直緻力于流體動力學方程研究，在描述複雜流動的非線性偏微分方程解的存在唯一性，正則性，衰減性，穩定性和動力學性态等方面做了一些較好的工作。董教授先後在Nonlinearity，J.Differential Equations，Discrete Contin. Dyn. Syst， J. Math. Phys等重要國際期刊上發表SCI收錄論文40餘篇，研究工作被國内外同行在主流期刊上SCI他引100餘次，曾主持多項國家自然科學基金項目。
時 間：2017年6月13日（周二）下午4：30始
地 點：南海樓224室
熱烈歡迎廣大師生參加!
太阳集团1088vip/網絡空間安全學院
2017年6月9日