Communications in Mathematical Sciences

Volume 14 (2016)

Number 3

Attractor of the quantum Zakharov system on an unbounded domain

Pages: 627 – 641

DOI: http://dx.doi.org/10.4310/CMS.2016.v14.n3.a2

Authors

Yanfeng Guo (School of Science, Guangxi University of Science and Technology, Liuzhou, Guangxi, China)

Jingjun Zhang (College of Mathematics, Physics and Information Engineering, Jiaxing University, Jiaxing, Zhejiang, China)

Chunxiao Guo (Department of Mathematics, China University of Mining and Technology, Beijing, China)

Abstract

In this paper, we study the attractor of the quantum Zakharov system on unbounded domain $\mathbb{R}^d (d=1,2,3)$. We first prove the existence and uniqueness of the solution by the standard energy method. Then, by making use of the particular characters of the quantum Zakharov system and the special decomposition of the solution operator, we obtain the existence of an attractor for this system.

Keywords

quantum Zakharov system, existence and uniqueness, attractor, decomposition

2010 Mathematics Subject Classification

35Q35, 60H15, 76A05

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Published 26 February 2016