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The radial defocusing energy-supercritical NLS in dimension four (2104.15035v2)
Published 30 Apr 2021 in math.AP
Abstract: We consider the radial defocusing nonlinear Schr\"odinger equations $iu_t+\Delta u=|u|{p}u$ with supercritical exponent $p>4$ in four space dimensions, and prove that any radial solution that remains bounded in the critical Sobolev space must be global and scatter.