On the nonlinear regularized Schrödinger equation in exterior domains

Abstract

In this paper, we will establish, in two and three dimensions, the local well-posedness result in $H_0^1\left(\mathrm{\Omega }\right)$ of the nonlinear regularized Schrödinger equation using the Strichartz estimates for the regularized Schrödinger equation on exterior domains established previously. Then, we will prove, the global existence and uniqueness result in $L^2\left(\mathrm{\Omega }\right)$.