The existence of global strong and weak solutions for the Novikov equation
The well-posedness of the global strong and weak solutions for the Novikov equation is investigated. Provided that initial value u0 ∈ Hs(s > 3/2) and satisfying a sign condition, the existence and uniqueness of global strong solutions for the equation are shown to be valid in Sobolev space. The e...
| Main Authors: | , , |
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| Format: | Journal Article |
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Academic Press
2013
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| Online Access: | http://hdl.handle.net/20.500.11937/39165 |
| _version_ | 1848755517284941824 |
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| author | Lai, Shaoyong Li, Nan Wu, Yong Hong |
| author_facet | Lai, Shaoyong Li, Nan Wu, Yong Hong |
| author_sort | Lai, Shaoyong |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | The well-posedness of the global strong and weak solutions for the Novikov equation is investigated. Provided that initial value u0 ∈ Hs(s > 3/2) and satisfying a sign condition, the existence and uniqueness of global strong solutions for the equation are shown to be valid in Sobolev space. The estimates in Hq(R) space with 0≤q≤1/2, which are derived from the equation itself, are developed to prove the existence and uniqueness of the global weak solutions. |
| first_indexed | 2025-11-14T08:57:34Z |
| format | Journal Article |
| id | curtin-20.500.11937-39165 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T08:57:34Z |
| publishDate | 2013 |
| publisher | Academic Press |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-391652017-09-13T15:59:13Z The existence of global strong and weak solutions for the Novikov equation Lai, Shaoyong Li, Nan Wu, Yong Hong The Novikov equation Global weak solution Global strong solution Well-posedness The well-posedness of the global strong and weak solutions for the Novikov equation is investigated. Provided that initial value u0 ∈ Hs(s > 3/2) and satisfying a sign condition, the existence and uniqueness of global strong solutions for the equation are shown to be valid in Sobolev space. The estimates in Hq(R) space with 0≤q≤1/2, which are derived from the equation itself, are developed to prove the existence and uniqueness of the global weak solutions. 2013 Journal Article http://hdl.handle.net/20.500.11937/39165 10.1016/j.jmaa.2012.10.048 Academic Press unknown |
| spellingShingle | The Novikov equation Global weak solution Global strong solution Well-posedness Lai, Shaoyong Li, Nan Wu, Yong Hong The existence of global strong and weak solutions for the Novikov equation |
| title | The existence of global strong and weak solutions for the Novikov equation |
| title_full | The existence of global strong and weak solutions for the Novikov equation |
| title_fullStr | The existence of global strong and weak solutions for the Novikov equation |
| title_full_unstemmed | The existence of global strong and weak solutions for the Novikov equation |
| title_short | The existence of global strong and weak solutions for the Novikov equation |
| title_sort | existence of global strong and weak solutions for the novikov equation |
| topic | The Novikov equation Global weak solution Global strong solution Well-posedness |
| url | http://hdl.handle.net/20.500.11937/39165 |