Analysis & PDE
- Anal. PDE
- Volume 4, Number 2 (2011), 341-367.
Well- and ill-posedness issues for energy supercritical waves
We investigate the initial value problem for some energy supercritical semilinear wave equations. We establish local existence in suitable spaces with continuous flow. The proof uses the finite speed of propagation and a quantitative study of the associated ODE. It does not require any scaling invariance of the equation. We also obtain some ill-posedness and weak ill-posedness results.
Anal. PDE, Volume 4, Number 2 (2011), 341-367.
Received: 6 December 2009
Revised: 31 May 2010
Accepted: 29 June 2010
First available in Project Euclid: 20 December 2017
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Ibrahim, Slim; Majdoub, Mohamed; Masmoudi, Nader. Well- and ill-posedness issues for energy supercritical waves. Anal. PDE 4 (2011), no. 2, 341--367. doi:10.2140/apde.2011.4.341. https://projecteuclid.org/euclid.apde/1513731128