Acta mathematica scientia,Series B ›› 2016, Vol. 36 ›› Issue (2): 371-384.doi: 10.1016/S0252-9602(16)30006-6

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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.

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

CLC Number: 

  • 35A05
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