The defocusing energy-supercritical cubic nonlinear wave equation in dimension five
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.
Publication Source (Journal or Book title)
Transactions of the American Mathematical Society
Bulut, A. (2015). The defocusing energy-supercritical cubic nonlinear wave equation in dimension five. Transactions of the American Mathematical Society, 367 (9), 6017-6061. https://doi.org/10.1090/tran/6068