The defocusing energy-supercritical cubic nonlinear wave equation in dimension five
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Abstract:
We consider the energy-supercritical nonlinear wave equation $u_{tt}-\Delta u+|u|^2u=0$ 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 $d\geq 6$ 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.References
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Additional Information
- Aynur Bulut
- Affiliation: School of Mathematics, Institute for Advanced Study, Princeton, New Jersey 08540
- MR Author ID: 913497
- Email: abulut@math.ias.edu
- Received by editor(s): October 14, 2012
- Received by editor(s) in revised form: December 23, 2012
- Published electronically: April 20, 2015
- © Copyright 2015 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 367 (2015), 6017-6061
- MSC (2010): Primary 35L71, 35B44, 35P25
- DOI: https://doi.org/10.1090/tran/6068
- MathSciNet review: 3356928