Regularity criteria for the Navier–Stokes equations based on one component of velocity. (June 2017) - Guo, Zhengguang; Caggio, Matteo; Skalák, Zdeněk
Abstract: We study the regularity criteria for the incompressible Navier–Stokes equations in the whole space R 3 based on one velocity component, namely u 3, ∇ u 3 and ∇ 2 u 3 . We use a generalization of the Troisi inequality and anisotropic Lebesgue spaces and prove, for example, that the condition ∇ u 3 ∈ L β ( 0, T ; L p ), where 2 / β + 3 / p = 7 / 4 + 1 / ( 2 p ) and p ∈ ( 2, ∞ ], yields the regularity of u on ( 0, T ] .