Stability of a coupled wave-Klein-Gordon system with quadratic nonlinearities

Abstract

Using the hyperboloidal foliation method, we establish stability results for a coupled wave-Klein-Gordon system with quadratic nonlinearities. In particular, we investigate quadratic wave-Klein-Gordon interactions in which there are no derivatives on the massless wave component. By combining hyperboloidal energy estimates with appropriate transformations of our fields, we are able to show global existence of solutions for sufficiently small initial data.

arXiv commentPublished version. Both authors are grateful to the anonymous referees, whose comments improve a lot on the presentation and the precision of the article

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• Almost global well-posedness for quasilinear strongly coupled wave-Klein-Gordon systems in two space dimensions
• Two dimensional wave--Klein-Gordon equations with semilinear nonlinearities
• Stability of a wave and Klein-Gordon system with mixed coupling
• Global well-posedness for a system of quasilinear wave equations on a product space
• From Klein-Gordon-Wave to Schrödinger-Wave: a Normal Form Approach