On the Critical One Components Regularity for the $3-D$ Navier-Stokes System in $L_T^p({\dot{B}}_{2,\infty }^{\frac{1}{2}+\frac{2}{p}})$ spaces

Wei Luo, Zhanyang Yin, Pei Zheng

We consider the conditional regularity of the mild solution $v$ of the $3-D$ incompressible Navier-Stokes equations with initial data $v_0\in {\dot{H}}^{\frac{1}{2}}$ and vorticity $Ω_…