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In this work we consider the problem of global existence of small regularsolutions to a type nonlinear wave-Klein-Gordon system with semi-linearinteractions in two spatial dimension. We develop some new techniques on bothwave equations and Klein-Gordon equations in order to get sufficient decayrates when energies are not uniformly bounded. These techniques are compatiblewith those introduced in previous work on two spatial-dimensional quasi-linearwave-Klein-Gordon systems, and can be applied in much general cases.

Global solutions of non-linear wave-Klein-Gordon system in two space dimension: semi-linear interactions