Analysis & PDE
Anal. PDE
Volume 8, Number 2 (2015), 467-497.
Scattering for the radial 3D cubic wave equation
Benjamin Dodson and Andrew Lawrie
More by Benjamin Dodson
More by Andrew Lawrie
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Consider the Cauchy problem for the radial cubic wave equation in 1 + 3 dimensions with either the focusing or defocusing sign. This problem is critical in Ḣ1∕2 ×Ḣ−1∕2(ℝ3) and subcritical with respect to the conserved energy. Here we prove that if the critical norm of a solution remains bounded on the maximal time interval of existence, then the solution must in fact be global in time and must scatter to free waves as t →±∞.
Anal. PDE, Volume 8, Number 2 (2015), 467-497.
Revised: 12 October 2014
First available in Project Euclid: 16 November 2017
https://projecteuclid.org/euclid.apde/1510843075
doi:10.2140/apde.2015.8.467
Primary: 35L05: Wave equation
scattering concentration compactness double Duhamel
Dodson, Benjamin; Lawrie, Andrew. Scattering for the radial 3D cubic wave equation. Anal. PDE 8 (2015), no. 2, 467--497. doi:10.2140/apde.2015.8.467. https://projecteuclid.org/euclid.apde/1510843075
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