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We consider the coupled systems of nonlinear wave and Klein-Gordon equationsin two space dimensions with cubic nonlinearity. For this kind of systems, thesmall data global existence is already known if the cubic nonlinearitysatisfies a certain condition related to the null condition. In this article,our aim is to investigate the small data global existence under a conditionrelated to the weak null condition. We also make a remark on the asymptoticbehavior of global solutions.

Global existence for systems of nonlinear wave and Klein-Gordon equations in two space dimensions under a kind of the weak null condition