Global Analysis for Rough Solutions to the Davey-Stewartson System
The global well-posedness of rough solutions to the Cauchy problem for the Davey-Stewartson system is obtained. It reads that if the initial data is in Hs with s > 2/5, then there exists a global solution in time, and the Hs norm of the solution obeys polynomial-in-time bounds. The new ingredient...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/578701 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832567652401283072 |
|---|---|
| author | Han Yang Xiaoming Fan Shihui Zhu |
| author_facet | Han Yang Xiaoming Fan Shihui Zhu |
| author_sort | Han Yang |
| collection | DOAJ |
| description | The global well-posedness of rough solutions to the Cauchy problem for the Davey-Stewartson system is obtained. It reads that if
the initial data is in Hs with s > 2/5, then there exists a global solution in time, and the Hs norm of the solution obeys polynomial-in-time bounds. The new
ingredient in this paper is an interaction Morawetz estimate, which generates a new space-time Lt,x4 estimate for nonlinear equation with the relatively general defocusing power nonlinearity. |
| format | Article |
| id | doaj-art-61cb106048b1461cb2a23a7997ea0c29 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-61cb106048b1461cb2a23a7997ea0c292025-02-03T01:00:52ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/578701578701Global Analysis for Rough Solutions to the Davey-Stewartson SystemHan Yang0Xiaoming Fan1Shihui Zhu2College of Mathematics, Southwest Jiaotong University, Chengdu 610031, ChinaCollege of Mathematics, Southwest Jiaotong University, Chengdu 610031, ChinaCollege of Mathematics and Software Science, Sichuan Normal University, Chengdu 610066, ChinaThe global well-posedness of rough solutions to the Cauchy problem for the Davey-Stewartson system is obtained. It reads that if the initial data is in Hs with s > 2/5, then there exists a global solution in time, and the Hs norm of the solution obeys polynomial-in-time bounds. The new ingredient in this paper is an interaction Morawetz estimate, which generates a new space-time Lt,x4 estimate for nonlinear equation with the relatively general defocusing power nonlinearity.http://dx.doi.org/10.1155/2012/578701 |
| spellingShingle | Han Yang Xiaoming Fan Shihui Zhu Global Analysis for Rough Solutions to the Davey-Stewartson System Abstract and Applied Analysis |
| title | Global Analysis for Rough Solutions to the Davey-Stewartson System |
| title_full | Global Analysis for Rough Solutions to the Davey-Stewartson System |
| title_fullStr | Global Analysis for Rough Solutions to the Davey-Stewartson System |
| title_full_unstemmed | Global Analysis for Rough Solutions to the Davey-Stewartson System |
| title_short | Global Analysis for Rough Solutions to the Davey-Stewartson System |
| title_sort | global analysis for rough solutions to the davey stewartson system |
| url | http://dx.doi.org/10.1155/2012/578701 |
| work_keys_str_mv | AT hanyang globalanalysisforroughsolutionstothedaveystewartsonsystem AT xiaomingfan globalanalysisforroughsolutionstothedaveystewartsonsystem AT shihuizhu globalanalysisforroughsolutionstothedaveystewartsonsystem |