Regularity criteria for the Navier-Stokes equations based on one component of velocity

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• 作者：Zhengguang Guo^a ; ^{gzgmath@wzu.edu.cn} ; Matteo Caggio^b ; ^{caggio@kma.zcu.cz} ; Zdeněk Skalá ; k^c ; ^{zdenek.skalak@cvut.cz}
• 关键词：Navier&ndash ; Stokes equations ; Regularity of solutions ; Regularity criteria ; Anisotropic Lebesgue spaces
• 刊名：Nonlinear Analysis: Real World Applications
• 出版年：2017
• 出版时间：June 2017
• 年：2017
• 卷：35
• 期：Complete
• 页码：379-396
• 全文大小：678 K
• 卷排序：35

文摘

We study the regularity criteria for the incompressible Navier–Stokes equations in the whole space R3R3 based on one velocity component, namely u3u3, ∇u3∇u3 and ∇2u3∇2u3. We use a generalization of the Troisi inequality and anisotropic Lebesgue spaces and prove, for example, that the condition ∇u3∈Lβ(0,T;Lp)∇u3∈Lβ(0,T;Lp), where 2/β+3/p=7/4+1/(2p)2/β+3/p=7/4+1/(2p) and p∈(2,∞]p∈(2,∞], yields the regularity of uu on (0,T](0,T].