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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
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