Global solutions of wave-Klein-Gordon system in two spatial dimensions with strong couplings in divergence form

Abstract

In this paper we established the global well-posedness theorem for a special type of wave-Klein-Gordon system that have the strong coupling terms in divergence form on the right hand side of its wave equation. We cope with the problem by constructing an auxiliary system with the shifted primitives of the original unknowns. The result is then applied directly on Klein-Gordon-Zakharov system in 2+1 space-time with general small-localized-regular initial data. In the end of this paper, we also give a preliminary answer to the question of global stability of a class of totally geodesic the wave maps in 2+1 dimensional case.

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• Global stability of some totally geodesic wave maps
• Two dimensional wave--Klein-Gordon equations with semilinear nonlinearities
• 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