Global solutions of nonlinear wave-Klein-Gordon system in two spatial dimensions: weak coupling case

Abstract

In this article we will prove the global existence of a type of wave-Klein-Gordon system in $2+1$ spacetime dimension. Some technical tools such as conformal energy estimate on hyperboloid, normal form transform on Klein-Gordon equations will be adapted to this $2+1$ dimensional case.

arXiv comment48 pages

References in corpus (3)

• An intrinsic hyperboloid approach for Einstein Klein-Gordon equations
• Small data global existence and decay for two dimensional wave maps
• A conformal-type energy inequality on hyperboloids and its application to quasi-linear wave equation in ${\mathbb{R}}^{3+1}$

Cited by in corpus (9)

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• Global solution to the wave and Klein-Gordon system under null condition in dimension two
• Almost global well-posedness for quasilinear strongly coupled wave-Klein-Gordon systems in two space dimensions
• Global stability of some totally geodesic wave maps
• Global solutions of nonlinear wave-Klein-Gordon system in two spatial dimensions: A prototype of strong coupling case
• Two dimensional wave--Klein-Gordon equations with semilinear nonlinearities
• Stability of a class of semilinear waves in $2+1$ dimension under null condition
• Global existence for systems of nonlinear wave and Klein-Gordon equations in two space dimensions under a kind of the weak null condition
• Global Existence and Scattering of the Klein-Gordon-Zakharov System in Two Space Dimensions