The sharp threshold and limiting profile of blow-up solutions for a Davey–Stewartson system
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 variatio...
| Main Authors: | , , , |
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| Format: | Journal Article |
| Published: |
Academic Press
2011
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| Online Access: | http://hdl.handle.net/20.500.11937/27805 |
| _version_ | 1848752364915261440 |
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| author | Li, X. Zhang, J. Lai, S. Wu, Yong Hong |
| author_facet | Li, X. Zhang, J. Lai, S. Wu, Yong Hong |
| author_sort | Li, X. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T08:07:27Z |
| format | Journal Article |
| id | curtin-20.500.11937-27805 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T08:07:27Z |
| publishDate | 2011 |
| publisher | Academic Press |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-278052017-09-13T16:07:33Z The sharp threshold and limiting profile of blow-up solutions for a Davey–Stewartson system Li, X. Zhang, J. Lai, S. Wu, Yong Hong Minimal blow-up solutions Davey–Stewartson systems Blow-up profile Mass concentration 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. 2011 Journal Article http://hdl.handle.net/20.500.11937/27805 10.1016/j.jde.2010.10.022 Academic Press unknown |
| spellingShingle | Minimal blow-up solutions Davey–Stewartson systems Blow-up profile Mass concentration Li, X. Zhang, J. Lai, S. Wu, Yong Hong The sharp threshold and limiting profile of blow-up solutions for a Davey–Stewartson system |
| title | The sharp threshold and limiting profile of blow-up solutions for a Davey–Stewartson system |
| title_full | The sharp threshold and limiting profile of blow-up solutions for a Davey–Stewartson system |
| title_fullStr | The sharp threshold and limiting profile of blow-up solutions for a Davey–Stewartson system |
| title_full_unstemmed | The sharp threshold and limiting profile of blow-up solutions for a Davey–Stewartson system |
| title_short | The sharp threshold and limiting profile of blow-up solutions for a Davey–Stewartson system |
| title_sort | sharp threshold and limiting profile of blow-up solutions for a davey–stewartson system |
| topic | Minimal blow-up solutions Davey–Stewartson systems Blow-up profile Mass concentration |
| url | http://hdl.handle.net/20.500.11937/27805 |