Homogenization for the cubic nonlinear Schr\"odinger equation on ${\mathbb{R}}^2$

We study the defocusing inhomogeneous mass-critical nonlinear Schr"odinger equation on ${\mathbb{R}}^2$ $$i{u}_t+\mathrm{\Delta }u=g(nx)\mathrm{\mid }u{\mathrm{\mid }}^{2}u$$ for initial data in $L^2({\mathbb{R}}^2)$. We obtain sufficient conditions on $g$ to ensure existence and uniqueness of global solutions for $n$ sufficiently large, as well as homogenization.