Title: Regularity criteria for the Navier-Stokes equations based on one component of velocity Authors: Guo, ZhengguangCaggio, MatteoSkalak, Zdenek Citation: GUO, Z., CAGGIO, M., SKALAK, Z. Regularity criteria for the Navier-Stokes equations based on one component of velocity. Nonlinear analysis-real world applications, 2017, roč. 35, č. JUN 2017, s. 379-396. ISSN 1468-1218. Issue Date: 2017 Publisher: Elsevier Document type: článekarticle URI: http://hdl.handle.net/11025/29184 ISSN: 1468-1218 Keywords in different language: Navier–Stokes equations Regularity of solutions Regularity criteria Anisotropic Lebesgue spaces Abstract in different language: We study the regularity criteria for the incompressible Navier-Stokes equations in the whole space $\mathbb{R}^3$ based on one velocity component, namely $u_3$, $\nabla u_3$ and $\nabla^2 u_3$. We use a generalization of the Troisi inequality and anisotropic Lebesgue spaces and prove, for example, that the condition $\nabla u_3 \in L^\beta(0,T;L^p)$, where $2/\beta + 3/p = 7/4+1/(2p)$ and $p\in (2,\infty]$, yields the regularity of $u$ on $(0,T]$. Rights: Plný text není přístupný.© Elsevier Appears in Collections: Články / Articles (KMA)OBD

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