Abstract
Abstract We consider the Zakharov system with quantum effects in the framework of the scalar mode in two space dimensions iEt + ΔE = nE + ΓΔ2E, nt = −∇ · V, (ZSQ) Vt = −∇n − ∇|E|2 + Γ∇Δn, which is related to quantum corrections to the Zakharov system for Langmuir waves in plasma. We prove the existence and uniqueness of global smooth solutions to the Cauchy problem for (ZSQ) in the Sobolev space through making a priori integral esimates and utilizing the so-called continuity method.
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