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

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