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On the Global Well-Posedness and Orbital Stability of Standing Waves for the Schrödinger Equation with Fractional Dissipation
In this paper, we are concerned with the nonlinear fractional Schrödinger equation. We extend the result of Guo and Huo and prove that the Cauchy problem of the nonlinear fractional Schrödinger equation is global well-posed in H32−γ(R) with 12≤γ<1. In view of the complexity of the nonlinear fractional Schrödinger equation …