Zhou, Yong A new regularity criterion for the Navier-Stokes equations in terms of the gradient of one velocity component. (English) Zbl 1166.35359 Methods Appl. Anal. 9, No. 4, 563-578 (2002). Summary: We consider the regularity criteria for the weak solutions to the Navier-Stokes equations in \(\mathbb{R}^3\). It is proved that if the gradient of any one component of the velocity field belongs to \(L^{\alpha,\gamma}\) with \(2/\alpha + 3/\gamma = 3/2\), \(3\leq\gamma < \infty\), then the weak solution actually is strong. Cited in 1 ReviewCited in 63 Documents MSC: 35Q30 Navier-Stokes equations 35B65 Smoothness and regularity of solutions to PDEs 76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids 76D05 Navier-Stokes equations for incompressible viscous fluids PDFBibTeX XMLCite \textit{Y. Zhou}, Methods Appl. Anal. 9, No. 4, 563--578 (2002; Zbl 1166.35359) Full Text: DOI