Abstract:

The Rayleigh-Taylor (RT) instability is well known as gravity-driven instability in fluids when a heavy fluid is on top of a light one. It appears in a wide range of applications in science and technology, such as in inertia confinement fusion, Tokamak, Z-pinch, supernova explosions. In this talk, mathematical analysis of the magnetic RT instability will be presented, in particular, effects of (impressed) magnetic fields upon the growth of the RT instability will be discussed and analyzed quantitatively. In particular, this talk will focus on compressible magnetohydrodynamic (MHD) flows. We shall show that a sufficiently strong (impressed) magnetic field can inhibit the RT instability; otherwise, instability will still occur in the sense that solutions do not continuously depend on initial data. Moreover, different (sharp) criteria on the strength of magnetic fields which guarantee stability will be compared and analyzed from both mathematical and physical points of view.  

Introduction of the Speaker：

Professor Song Jiang is a member of the Chinese Academy of Science, a research fellow of the Institute of Applied Physics and Computational Mathematics in Beijing, and a famous applied mathematician. He majors in the mathematical theories, numerical methods and applications of compressible fluid mechanics. He has made a series of achievements in many fields, such as the well-posedness theory of the compressible Navier-Stokes equation, Reyleigh-Taylor instability of fluid and magnetofluid, and mathematical analysis for small Mach limit. In the application, Professor Jiang and his colleagues have put forward many new practical algorithms, like the whole ALE and local Euler coupling method, to overcome the computational difficulties in the numerical simulation of weapons' physical properties, and developed a numerical simulation software platform for heavy weapons. Professor Jiang has won many awards, including the second prize of China's State Natural Science Award, the first prize of Military Progress Award in Science and Technology, the Chinese Youth Prize for Science and Technology and the Qiushi Youth Award.