On the vanishing viscosity limit for the 3D Navier‐Stokes equations with a slip boundary condition
On the vanishing viscosity limit for the 3D Navier‐Stokes equations with a slip boundary condition
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DOI：
10.1002/cpa.20187
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发表时间：
2007-07
影响因子：
3
通讯作者：
Yue-long Xiao;Z. Xin
中科院分区：
文献类型：
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作者：
Yue-long Xiao;Z. Xin
其中∇·和∇×分别表示div和curl算子，n是向外法线，τ是∂Ω的单位切向向量。在二维和三维情况下研究纳维-斯托克斯方程解的消失粘度极限是一个经典问题。由此产生两个相关的问题：一是如何描述纳维-斯托克斯方程的无粘极限行为；二是如何描述纳维-斯托克斯方程的无粘极限行为。二是欧拉方程是否可以用纳维-斯托克斯方程来近似。 ＊本研究的解决方案部分由郑格儒基金会、香港研究资助局专项研究资助金 CUHK-4028/04P、CUHK-4040/02P 和 CUHK-4279/00P 资助。
where and below ∇· and ∇× denote the div and curl operators respectively, n is the outward normal, and τ is the unit tangential vector of ∂Ω. The investigation of vanishing viscosity limit of solutions of the Navier-Stokes equations both in the two and three spacial dimensional cases is a classical issue. There are two related questions arising from here: one is how to describe the inviscid limiting behavior of the Navier-Stokes equation; and the other is that does the Euler equation can be approximated by the Navier-Stokes equations. In the case that the solution to the ∗This research is supported in part by Zheng Ge Ru Foundation, and Hong Kong RGC Earmarked Research Grants CUHK-4028/04P, CUHK-4040/02P and CUHK-4279/00P.