学术报告
On stabilizing effect of the magnetic fields in the Rayleigh-Taylor and Parker instabilities- Prof. Song Jiang（Institute of Applied Physics and Computational Mathematics, Beijing, China)
题目: On stabilizing effect of the magnetic fields in the Rayleigh-Taylor and Parker instabilities
报告人: Prof. Song Jiang
（Institute of Applied Physics and Computational Mathematics, Beijing, China)
摘要：We investigate the stabilizing effect of the vertical equilibrium magnetic field in the Rayleigh-Taylor (RT) problem for a nonhomogeneous incompressible viscous magnetohydrodynamic (MHD) fluid of zero resistivity in the presence of a uniform gravitational field in a horizontally periodic domain, in which the velocity of the fluid is non-slip on both upper and lower flat boundaries When an initial perturbation around a magnetic RT equilibrium state satisfies some relations, and the strength of the vertical magnetic field of the equilibrium state is bigger than the critical number we can use the Bogovskii function in the standing-wave form and adapt a two-tier energy method in Lagrangian coordinates to show the existence of a unique global-in-time (perturbed) stability solution to the magnetic RT problem. For the case that the strength of the vertical magnetic field is smaller than the critical number, by developing new analysis techniques based on the method of bootstrap instability, we show that the nonlinear RT instability will occur. The current result reveals from the mathematical point of view that the sufficiently large vertical equilibrium magnetic field has a stabilizing effect and can prevent the RT instability in MHD flows from occurring. Similar conclusions can be also verified for the horizontal magnetic field when the domain is vertically periodic. For the compressible MHD case, we shall discuss the Parker instability arising from astrophysics and also analyze the stabilizing effect of the magnetic fields. (joint work with Fei Jiang)
时间：2016年9月21日（周三）4:00-5:00
地点：首都师大北二区教学楼508教室
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