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. We also obtain some ill-posedness/weak ill-posedness results. 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.
Mathematics - Analysis of PDEs, Mathematics - Classical Analysis and ODEs, 35L05, 49K40, 65F22, 34-XX, 34Cxx, 34C25