On the convergence of the solution for a reduced model of the vectorial quantum Zakharov system

Abstract

In this paper, we study the limit behavior of the smooth solution for a reduced vectorial quantum Zakharov system which describes the interaction between the quantum Langmuir waves and quantum ion-acoustic waves in the plasmas. We first give the local existence and uniqueness of the solution to the quantum Zakharov system. Then we derive the uniform bounds of solution with appropriate initial data, and prove that the solution of the quantum Zakharov system converges to the solution of the nonlinear Schrödinger system.