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The sharp threshold and limiting profile of blow-up solutions for a Davey-Stewartson system. (English) Zbl 1228.35067
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.
MSC:
35B44Blow-up (PDE)
35L05Wave equation (hyperbolic PDE)
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