The defocusing energy-supercritical cubic nonlinear wave equation in dimension five

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We consider the energy-supercritical nonlinear wave equation utt− Δu + |u|2u = 0 with defocusing cubic nonlinearity in dimension d = 5 with no radial assumption on the initial data. We prove that a uniform-in-time a priori bound on the critical norm implies that solutions exist globally in time and scatter at infinity in both time directions. Together with our earlier works in dimensions d ≥ 6 with general data and dimension d = 5 with radial data, the present work completes the study of global well-posedness and scattering in the energy-supercritical regime for the cubic nonlinearity under the assumption of uniform-in-time control over the critical norm.

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Transactions of the American Mathematical Society

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