INHOMOGENEOUS DIRICHLET-BOUNDARY VALUE PROBLEM FOR TWO-DIMENSIONAL QUADRATIC NONLINEAR SCHRÖDINGER EQUATIONS

Abstract

We consider the inhomogeneous Dirichlet-boundary value problem for the quadratic nonlinear Schrödinger equations, which is considered as a critical case for the large-time asymptotics of solutions. We present sufficient conditions on the initial and boundary data which ensure asymptotic behavior of small solutions to the equations by using the classical energy method and factorization techniques of the free Schrödinger group.