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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/578701 |
| Summary: | 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. |
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| ISSN: | 1085-3375 1687-0409 |