Analysis & PDE
- Anal. PDE
- Volume 2, Number 3 (2009), 261-280.
Global existence of smooth solutions of a 3D log-log energy-supercritical wave equation
We prove global existence of smooth solutions of the 3D log-log energy-supercritical wave equation
with and smooth initial data . First we control the norm of the solution on an arbitrary size time interval by an expression depending on the energy and an a priori upper bound of its norm, with . The proof of this long time estimate relies upon the use of some potential decay estimates and a modification of an argument by Tao. Then we find an a posteriori upper bound of the norm of the solution by combining the long time estimate with an induction on time of the Strichartz estimates.
Anal. PDE, Volume 2, Number 3 (2009), 261-280.
Received: 4 November 2008
Revised: 7 June 2009
Accepted: 21 July 2009
First available in Project Euclid: 20 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10]
Roy, Tristan. Global existence of smooth solutions of a 3D log-log energy-supercritical wave equation. Anal. PDE 2 (2009), no. 3, 261--280. doi:10.2140/apde.2009.2.261. https://projecteuclid.org/euclid.apde/1513798037