Transfer of global wellposedness from nonlinear Klein-Gordon equation to nonlinear Schrödinger equation. (English) Zbl 1184.35215
Summary: We discuss relations between the nonlinear Klein-Gordon equation and the nonlinear Schrödinger equation in view of the global wellposedness in the energy space and \(L^2\). In some critical cases, we show that the global wellposedness for the former equation with some uniform bounds implies that for the latter.
MSC:
35L71 | Second-order semilinear hyperbolic equations |
35Q55 | NLS equations (nonlinear Schrödinger equations) |
35B40 | Asymptotic behavior of solutions to PDEs |
35B25 | Singular perturbations in context of PDEs |