Nonlinear Schrödinger Equations in the Sobolev Space of Critical Order

Abstract

The Cauchy problem for the nonlinear Schrödinger equations is considered in the Sobolev spaceHn/2(Rn) of critical ordern/2, where the embedding intoL∞(Rn) breaks down and any power behavior of interaction works as a subcritical nonlinearity. Under the interaction of exponential type the existence and uniqueness is proved for globalHn/2-solutions with small Cauchy data. © 1998 Academic Press.