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On regularity criteria for the 3D Navier-Stokes equations involving the ratio of the vorticity and the velocity. (English) Zbl 1372.35220
Summary: This note concerns regularity criteria for the Navier-Stokes equations. It is proved that if the solution satisfies \(\int_0^T\frac{\|\omega(\tau)\|_{L^s}^{\frac{2s}{2s-3}}}{\| \mathbf u(\tau)\|_{L^3}^{f(s)}}\mathrm d\tau<\infty\) for \(\frac{3}{2}<s<\infty\) and suitable function \(f(s)\), then the solution is regular on \((0,T]\).

35Q30 Navier-Stokes equations
35B65 Smoothness and regularity of solutions to PDEs
76D05 Navier-Stokes equations for incompressible viscous fluids
Full Text: DOI
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