The Viscous Surface-Internal Wave Problem: Global Well-Posedness and Decay

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	The Viscous Surface-Internal Wave Problem: Global Well-Posedness and Decay
	Wang, Yanjin ; Tice, Ian ; Kim, Chanwoo ; Wang YJ(王焰金)
刊名	http://dx.doi.org/10.1007/s00205-013-0700-2
	2014
关键词	NAVIER-STOKES EQUATIONS LARGE-TIME EXISTENCE INCOMPRESSIBLE FLUID TENSION MOTION FLOW
英文摘要	China Scholarship Council; We consider the free boundary problem for two layers of immiscible, viscous, incompressible fluid in a uniform gravitational field, lying above a general rigid bottom in a three-dimensional horizontally periodic setting. We establish the global well-posedness of the problem both with and without surface tension. We prove that without surface tension the solution decays to the equilibrium state at an almost exponential rate; with surface tension, we show that the solution decays at an exponential rate. Our results include the case in which a heavier fluid lies above a lighter one, provided that the surface tension at the free internal interface is above a critical value, which we identify. This means that sufficiently large surface tension stabilizes the Rayleigh-Taylor instability in the nonlinear setting. As a part of our analysis, we establish elliptic estimates for the two-phase stationary Stokes problem.
语种	英语
出版者	SPRINGER
内容类型	期刊论文
源URL	[http://dspace.xmu.edu.cn/handle/2288/91355]
专题	数学科学－已发表论文
推荐引用方式 GB/T 7714	Wang, Yanjin,Tice, Ian,Kim, Chanwoo,et al. The Viscous Surface-Internal Wave Problem: Global Well-Posedness and Decay[J]. http://dx.doi.org/10.1007/s00205-013-0700-2,2014.
APA	Wang, Yanjin,Tice, Ian,Kim, Chanwoo,&王焰金.(2014).The Viscous Surface-Internal Wave Problem: Global Well-Posedness and Decay.http://dx.doi.org/10.1007/s00205-013-0700-2.
MLA	Wang, Yanjin,et al."The Viscous Surface-Internal Wave Problem: Global Well-Posedness and Decay".http://dx.doi.org/10.1007/s00205-013-0700-2 (2014).