数学物理学报(英文版) ›› 2016, Vol. 36 ›› Issue (2): 371-384.doi: 10.1016/S0252-9602(16)30006-6

• 论文 • 上一篇    下一篇

ON THE CAUCHY PROBLEM OF A COHERENTLY COUPLED SCHRÖDINGER SYSTEM

王忠, 崔尚斌   

  1. Department of Mathematics, Sun Yat-Sen University, Guangzhou 510275, China
  • 收稿日期:2013-12-11 修回日期:2015-08-06 出版日期:2016-04-25 发布日期:2016-04-25
  • 作者简介:Zhong WANG,E-mail:wangzh79@mail2.sysu.edu.cn;Shangbin CUI,E-mail:cuishb@mail.sysu.edu.cn
  • 基金资助:

    This work is supported by the China National Natural Science Foundation under grant number 11171357.

ON THE CAUCHY PROBLEM OF A COHERENTLY COUPLED SCHRÖDINGER SYSTEM

Zhong WANG, Shangbin CUI   

  1. Department of Mathematics, Sun Yat-Sen University, Guangzhou 510275, China
  • Received:2013-12-11 Revised:2015-08-06 Online:2016-04-25 Published:2016-04-25
  • Supported by:

    This work is supported by the China National Natural Science Foundation under grant number 11171357.

摘要:

In this article, we consider the well-posedness of a coherently coupled Schrödinger system with four waves mixing in space dimension n≤4. The Cauchy problem for the cubic system is studied in L2 for n≤2 and in H1 for n≤4. We obtain two sharp conditions between global existence and blow up.

关键词: Cauchy problem, coherently, Schrödinger system, global existence

Abstract:

In this article, we consider the well-posedness of a coherently coupled Schrödinger system with four waves mixing in space dimension n≤4. The Cauchy problem for the cubic system is studied in L2 for n≤2 and in H1 for n≤4. We obtain two sharp conditions between global existence and blow up.

Key words: Cauchy problem, coherently, Schrödinger system, global existence

中图分类号: 

  • 35A05