  We prove that if $u(t)$ is a log-log blow-up solution, of the type studied by
Merle-Rapha\"el (2001-2005), to the $L^2$ critical focusing NLS equation
$i\partial_t u +\Delta u + |u|^{4/d} u=0$ with initial data $u_0\in
H^1(\mathbb{R}^d)$ in the cases $d=1, 2$, then $u(t)$ remains bounded in $H^1$
away from the blow-up point. This is obtained without assuming that the initial
data $u_0$ has any regularity beyond $H^1(\mathbb{R}^d)$. As an application of
the $d=1$ result, we construct an open subset of initial data in the radial
energy space $H^1_{rad}(\mathbb{R}^3)$ with corresponding solutions that
blow-up on a sphere at positive radius for the 3d quintic ($\dot H^1$-critical)
focusing NLS equation $i\partial_tu + \Delta u + |u|^4u=0$. This improves
Rapha\"el-Szeftel (2009), where an open subset in $H^3_{rad}(\mathbb{R}^3)$ is
obtained. The method of proof can be summarized as follows: on the whole space,
high frequencies above the blow-up scale are controlled by the bilinear
Strichartz estimates. On the other hand, outside the blow-up core, low
frequencies are controlled by finite speed of propagation.
