We consider a class of power-type nonlinear Schrödinger equations for which the power of the nonlinearity lies between the mass- and energy-critical exponents. Following the concentration-compactness approach, we prove that if a solution u is bounded in the critical Sobolev space throughout its lifespan, that is, u∈ Lₜ^∞ Ḣₓsc, then u is global and scatters.
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Jason Murphy (2014) studied this question.
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