Abstract
In this paper we investigate the small data global existence and pointwise decay of solutions to two systems of coupled wave-Klein–Gordon equations in two spatial dimensions. In particular, we consider critical (in the sense of time decay) semilinear nonlinearities for the wave equation and below-critical semilinear nonlinearities for the Klein–Gordon equation, a situation that has not been studied before in the context of coupled wave and Klein–Gordon equations. An interesting feature of our two systems is that the below-critical nonlinearity causes the Klein–Gordon field to lose its linear behaviour close to the light cone, even though it enjoys optimal time decay.
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