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Zbl 1228.35067
Li, Xiaoguang; Zhang, Jian; Lai, Shaoyong; Wu, Yonghong
The sharp threshold and limiting profile of blow-up solutions for a Davey-Stewartson system. (English)
[J] J. Differ. Equations 250, No. 4, 2197-2226 (2011). ISSN 0022-0396

The blow-up of solutions of the Cauchy problem for the Davey-Stawartson system, which is a model equation in the theory of shallow water waves, are investigated. Firstly, the existence of the ground state for the system derives the best constant of a Gagliardo-Nirenberg type inequality and the variational character of the ground state. Secondly, the blow-up threshold of the Davey-Stewartson system is developed. Thirdly, the mass concentration is established for all the blow-up solutions of the system.
[Shun-Tang Wu (Zhonghe)]

MSC 2000:: *35B44
35L05 Wave equation

Keywords: mass concentration; minimal blow-up solutions; Cauchy problem; shallow water waves

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