The anisotropic regularity criteria for 3D Navier–Stokes equations involving one velocity component

Publication date: August 2020Source: Nonlinear Analysis: Real World Applications, Volume 54Author(s): Chenyin QianAbstractThe anisotropic regularity criterion for the Navier–Stokes equations in terms of the one component of the velocity gradient (∂iuj,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 Dhαu3 with α∈[0,1] is also established, which can be reduced to some previous results with α=0 and α=1.

Source: Nonlinear Analysis: Real World Applications - January 21, 2020 Category: Research Source Type: research