The radial defocusing energy-supercritical NLS in dimension four
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radialdefocusingfourspaceboundedconsidercriticaldelta
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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.
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