Global existence for the damped Vlasov–Klein–Gordon system in the whole space

In this paper, we establish global existence of classical solutions for the damped two-species Vlasov-Klein-Gordon system in the whole space. We assume that the total positive charge nearly cancels out the total negative charge, even though the initial phase-space distribution of ions and electrons may be large. Mathematically, this scenario is often interpreted as the quasi-neutral condition. In reality, the quasi-neutral condition has a strong physical basis: it is well-known that the universe is predominantly composed of plasma, but since the total charges of positive and negative particles are approximately equal, the entire system remains electrically neutral.