Well- and ill-posedness issues for energy supercritical waves. (English) Zbl 1267.35131
Summary: 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.
MSC:
35L71 | Second-order semilinear hyperbolic equations |
49K40 | Sensitivity, stability, well-posedness |
65F22 | Ill-posedness and regularization problems in numerical linear algebra |
35R25 | Ill-posed problems for PDEs |