On the Rayleigh-Taylor Instability for the Incompressible Viscous Magnetohydrodynamic Equations

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	On the Rayleigh-Taylor Instability for the Incompressible Viscous Magnetohydrodynamic Equations
	Jiang, Fei ; Jiang, Song ; Wang, Yanjin ; Wang YJ(王焰金)
刊名	http://dx.doi.org/10.1080/03605302.2013.863913
	2014-03-04
英文摘要	NSFC [11101044, 11271051, 11301083, 11371065, 11201389]; National Basic Research Program [2011CB309705]; Natural Science Foundation of Fujian Province of China [2012J05011]; Specialized Research Fund for the Doctoral Program of Higher Education [20120121120023]; Fundamental Research Funds for the Central Universities [2013121002]; We study the Rayleigh-Taylor instability problem for two incompressible, immiscible, viscous magnetohydrodynamic (MHD) flows with zero resistivity and surface tension (or without surface tension), evolving with a free interface under presence of a uniform gravitational field. First, we reformulate the MHD free boundary problem in an infinite slab as a Navier-Stokes system in Lagrangian coordinates with a force term induced by the fluid flow map. Then, we analyze the linearized problem around the steady state which describes a denser immiscible fluid lying above a light one with a free interface separating the two fluids, and both fluids being in (unstable) equilibrium. By studying a family of modified variational problems, we construct smooth (when restricted to each fluid domain) solutions to the linearized problem that grow exponentially fast in time in Sobolev spaces, thus leading to an global instability result for the linearized problem. Finally, using these pathological solutions, we prove the global instability for the corresponding nonlinear problem in an appropriate sense. Moreover, we evaluate that the so-called critical number indeed is equal to root g[rho]/2, and analyze the effect of viscosity and surface tension on the instability.
语种	英语
出版者	TAYLOR & FRANCIS INC
内容类型	期刊论文
源URL	[http://dspace.xmu.edu.cn/handle/2288/91359]
专题	数学科学－已发表论文
推荐引用方式 GB/T 7714	Jiang, Fei,Jiang, Song,Wang, Yanjin,et al. On the Rayleigh-Taylor Instability for the Incompressible Viscous Magnetohydrodynamic Equations[J]. http://dx.doi.org/10.1080/03605302.2013.863913,2014.
APA	Jiang, Fei,Jiang, Song,Wang, Yanjin,&王焰金.(2014).On the Rayleigh-Taylor Instability for the Incompressible Viscous Magnetohydrodynamic Equations.http://dx.doi.org/10.1080/03605302.2013.863913.
MLA	Jiang, Fei,et al."On the Rayleigh-Taylor Instability for the Incompressible Viscous Magnetohydrodynamic Equations".http://dx.doi.org/10.1080/03605302.2013.863913 (2014).