We study regular solutions to wave equations with super-critical source terms, e.g., of exponent p > 5 in 3D. Such high-order sources have been a major challenge in the investigation of finite-energy (H1 × L2) solutions to wave PDEs for many years. The well-posedness question has been answered in part, but even the local existence, for instance, in 3 dimensions requires the relation p ≤ 6m/(m +...
