Acta mathematica scientia, Series B >
ON THE CAUCHY PROBLEM OF A COHERENTLY COUPLED SCHRÖDINGER SYSTEM
Received date: 2013-12-11
Revised date: 2015-08-06
Online published: 2016-04-25
Supported by
This work is supported by the China National Natural Science Foundation under grant number 11171357.
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
Zhong WANG , Shangbin CUI . ON THE CAUCHY PROBLEM OF A COHERENTLY COUPLED SCHRÖDINGER SYSTEM[J]. Acta mathematica scientia, Series B, 2016 , 36(2) : 371 -384 . DOI: 10.1016/S0252-9602(16)30006-6
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