Global Strong Solutions of the Coupled Klein-Gordon-Schrödinger Equations

Abstract

We study the initial-boundary value problem for the coupled Klein-Gordon-Schrödinger equations in a domain in R^N with N ≤ 4. Under natural assumptions on the initial data, we prove the existence and uniqueness of global solutions in H² ⊕ H² ⊕ H¹. The method of the construction of global strong solutions depends on the proof that solutions of regularized systems by the Yosida approximation form a bounded sequence in H² ⊕ H² ⊕ H¹ and a convergent sequence in H¹ ⊕ H¹ ⊕ L². The method of proof is independent of the Brezis-Gallouet technique and a compactness argument.