Cauchy problem of the generalized Zakharov type system in R 2 $\mathbf{R}^{2}$

Abstract

Abstract In this paper, we consider the initial value problem for a two-dimensional generalized Zakharov system with quantum effects. We prove the existence and uniqueness of global smooth solutions to the initial value problem in the Sobolev space through making a priori integral estimates and the Galerkin method.

Keywords

• Zakharov system
• Cauchy problem
• existence
• uniqueness