  We consider the mass supercritical (NLS) in dimension $d\ge 1$ in the
mass-supercritical range. The existence of self-similar blow up dyamics is
known [Merle-Rapha\"el-Szeftel, 2010], and suitable self-similar blow up
profiles were constructed [Bahri-Martel-Rapha\"el, 2021]. In this work, we
prove the finite codimensional nonlinear asymptotic stability of a large class
of self-similar profiles. The heart of the proof is, following the approach of
Beceanu [Beceanu, 2011], the derivation of Strichartz dispersive estimates for
matrix operators with a deformed Laplacian $\Delta_b = \Delta + ib\left(\frac
d2 + x\cdot\nabla\right)$ in homogeneous Sobolev spaces. The deformed Laplacian
$\Delta_b$ arises from the renormalization and its operator group
$e^{it\Delta_b}$ exhibits an "enhanced dispersion" phenomenon, which not only
recovers the free Strichartz but also enables an extension of resolvent
families. Compared with Strichartz estimates based on $\Delta$, this one has a
larger admissible region, works for arbitrarily small polynomial decaying
potential, and requires no spectral assumption.
