Almost global well-posedness for quasilinear strongly coupled wave-Klein-Gordon systems in two space dimensions
arXiv:1910.12673 · doi:10.1017/fms.2025.10081
Abstract
We prove almost global well-posedness for quasilinear strongly coupled wave-Klein-Gordon systems with small and localized data in two space dimensions. We assume only mild decay on the data at infinity as well as minimal regularity. We systematically investigate all the possible quadratic null form type quasilinear strong coupling nonlinearities, and provide a new, robust approach for the proof. In a second paper we will complete the present results to full global well-posedness.
52 pages, 2 figures. Fixed minor typos, added a proof for an interpolation lemma, now part of the Appendix
References in corpus (5)
- Stability of a coupled wave-Klein-Gordon system with quadratic nonlinearities
- An intrinsic hyperboloid approach for Einstein Klein-Gordon equations
- Global solutions of nonlinear wave-Klein-Gordon system in two spatial dimensions: weak coupling case
- Global solutions of non-linear wave-Klein-Gordon system in two space dimension: semi-linear interactions
- Global solutions of non-linear wave-Klein-Gordon system in one space dimension
Cited by in corpus (5)
- Global solution to the wave and Klein-Gordon system under null condition in dimension two
- Global stability of some totally geodesic wave maps
- Two dimensional wave--Klein-Gordon equations with semilinear nonlinearities
- Global solutions of nonlinear wave-Klein-Gordon system in two spatial dimensions: A prototype of strong coupling case
- Global well-posedness for a system of quasilinear wave equations on a product space