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.
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