Abstract:
We study the defocusing inhomogeneous mass-critical nonlinear Schrödinger equation on $\mathbb R^2$ $$i \partial_t u_n +\Delta u_n=g(nx) \abs{u_n}^2 u_n$$ 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.