The anisotropic regularity criteria for 3D Navier–Stokes equations involving one velocity component. (August 2020) - Qian, Chenyin
Abstract: The anisotropic regularity criterion for the Navier–Stokes equations in terms of the one component of the velocity gradient ( ∂ i u j, 1 ≤ i, j ≤ 3 ) is investigated. It is an improvement of results of Qian (2016) and is also a complement of the results of Guo et al. (2018) for i = j . Besides, the consistent regularity criterion without distinguishing i = j and i ≠ j is also obtained. Finally, the regularity result based on the fractional derivatives for one component of the velocity field D h α u 3 with α ∈ [ 0, 1 ] is also established, which can be reduced to some previous results with α = 0 and α = 1 .