On the Critical One Component Regularity for 3-D Navier-Stokes System: General Case

Let us consider initial data v(0) for the homogeneous incompressible 3D Navier-Stokes equation with vorticity belonging to L-3/2 boolean AND L-2. We prove that if the solution associated with v(0) blows up at a finite time T*, then for any p in ]4, infinity[, and any unit vector e of R-3, the L (p) norm in time with value in H (1/2) (+) (2/p) of (v|e) (3)(R) blows up at T*.MCM; National Center for Mathematics and Interdisciplinary Sciences; NSF of China [11371347, 11371037, 11425103]; Chinese Academy of Sciences; Program for New Century Excellent Talents in University; Fok Ying Tung Education FoundationSCI(E)ARTICLE3871-90522