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The sharp threshold and limiting profile of blow-up solutions for a Davey-Stewartson system |
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| Authors: | Xiaoguang Li Jian Zhang Yonghong Wu |
| Institution: | a Visual Computing and Virtual Reality Key Laboratory of Sichuan Province, Sichuan Normal University, Chengdu 610066, China b College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610066, China c Department of Applied Mathematics, Southwestern University of Finance and Economics, Chengdu 610074, China d Department of Mathematics and Statistics, Curtin University of Technology, Perth, WA 6845, Australia |
| Abstract: | The blow-up solutions of the Cauchy problem for the Davey-Stewartson 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 in R3. Thirdly, the mass concentration is established for all the blow-up solutions of the system in R2. Finally, the existence of the minimal blow-up solutions in R2 is constructed by using the pseudo-conformal invariance. The profile of the minimal blow-up solutions as t→T (blow-up time) is in detail investigated in terms of the ground state. |
| Keywords: | Davey-Stewartson systems Mass concentration Minimal blow-up solutions Blow-up profile |
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