## Analysis & PDE

• Anal. PDE
• Volume 8, Number 2 (2015), 467-497.

### Scattering for the radial 3D cubic wave equation

#### Abstract

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 $t →±∞$.

#### Article information

Source
Anal. PDE, Volume 8, Number 2 (2015), 467-497.

Dates
Revised: 12 October 2014
Accepted: 26 November 2014
First available in Project Euclid: 16 November 2017

https://projecteuclid.org/euclid.apde/1510843075

Digital Object Identifier
doi:10.2140/apde.2015.8.467

Mathematical Reviews number (MathSciNet)
MR3345634

Zentralblatt MATH identifier
1329.35206

Subjects
Primary: 35L05: Wave equation

#### Citation

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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