  In this paper, we study the $H^s$-stability of the log-log blowup regime
(which has been completely described in a series of recent works by Merle and
Raphael) for the focusing mass-critical nonlinear Schr\"odinger equations
$i\partial_tu+\Delta u+|u|^\frac4du=0$ in $\mathbb{R}^d$ with $d\geq3$. We aim
to extend the result in [Colliander and Raphael, Rough blowup solutions to the
$L^2$ critical NLS, Math. Anna., 345(2009), 307-366.] for dimension two to the
higher dimensions cases $d\geq3$, where we use the bootstrap argument in the
above paper and the commutator estimates in [M. Visan and X. Zhang, On the
blowup for the $L^2$-critical focusing nonlinear Schr\"odinger equation in
higher dimensions below the energy class. SIAM J. Math. Anal., 39(2007),
34-56.].
