  Let us consider an initial data $v_0$ for the homogeneous incompressible 3D
Navier-Stokes equation with vorticity belonging to $L^{\frac 32}\cap L^2$. We
prove that if the solution associated with $v_0$ blows up at a finite time
$T^\star$, then for any $p$ in $]4,\infty[$, and any unit vector $e$ of $\R^3$,
the $L^p$ norm in time with value in $\dot{H}^{\frac 12+\frac 2 p }$ of
$(v|e)_{\R^3}$ blows up at $T^\star$
