Two dimensional wave-Klein–Gordon equations with a below-critical nonlinearity

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