Global Smooth Solutions for the Zakharov System with Quantum Effects in Two Space Dimensions

作者：Gan Zaihui^*; Zhong Ting; Guo Boling

来源：Advanced Nonlinear Studies, 2014, 14(3): 687-707.

DOI：10.1515/ans-2014-0310

• Zakharov system
• Quantum effects
• Global solution
• Existence
• Uniqueness

We consider the Zakharov system with quantum effects in the framework of the scalar mode in two space dimensions
iE(t) + Delta E = nE + Gamma Delta E-2,
n(t) = -del . V, (ZSQ)
V-t = -del n - del vertical bar E vertical bar(2) + Gamma del Delta n,
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.

• 出版日期2014-8
• 单位天津大学; 北京应用物理与计算数学研究所; 四川师范大学