A Note on the Generalized Camassa-Holm Equation
We study the generalized Camassa-Holm equation which contains the Camassa-Holm (CH) equation and Novikov equation as special cases with the periodic boundary condition. We get a blow-up scenario and obtain the global existence of strong and weak solutions under suitable assumptions, respectively. Th...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
|
| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2014/975925 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832553193364520960 |
|---|---|
| author | Yun Wu Ping Zhao |
| author_facet | Yun Wu Ping Zhao |
| author_sort | Yun Wu |
| collection | DOAJ |
| description | We study the generalized Camassa-Holm equation which contains the Camassa-Holm (CH) equation and Novikov equation as special cases with the periodic boundary condition. We get a blow-up scenario and obtain the global existence of strong and weak solutions under suitable assumptions, respectively. Then, we construct the periodic peaked solutions and apply them to prove the ill-posedness in Hs with s<3/2. |
| format | Article |
| id | doaj-art-566be1b5615a4da3a8a23b1bfeaa40f2 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-566be1b5615a4da3a8a23b1bfeaa40f22025-02-03T05:54:38ZengWileyJournal of Function Spaces2314-88962314-88882014-01-01201410.1155/2014/975925975925A Note on the Generalized Camassa-Holm EquationYun Wu0Ping Zhao1Department of Mathematics and Computer Science, Guizhou Normal University, Guiyang, Guizhou 550001, ChinaDepartment of Mathematics and Computer Science, Guizhou Normal University, Guiyang, Guizhou 550001, ChinaWe study the generalized Camassa-Holm equation which contains the Camassa-Holm (CH) equation and Novikov equation as special cases with the periodic boundary condition. We get a blow-up scenario and obtain the global existence of strong and weak solutions under suitable assumptions, respectively. Then, we construct the periodic peaked solutions and apply them to prove the ill-posedness in Hs with s<3/2.http://dx.doi.org/10.1155/2014/975925 |
| spellingShingle | Yun Wu Ping Zhao A Note on the Generalized Camassa-Holm Equation Journal of Function Spaces |
| title | A Note on the Generalized Camassa-Holm Equation |
| title_full | A Note on the Generalized Camassa-Holm Equation |
| title_fullStr | A Note on the Generalized Camassa-Holm Equation |
| title_full_unstemmed | A Note on the Generalized Camassa-Holm Equation |
| title_short | A Note on the Generalized Camassa-Holm Equation |
| title_sort | note on the generalized camassa holm equation |
| url | http://dx.doi.org/10.1155/2014/975925 |
| work_keys_str_mv | AT yunwu anoteonthegeneralizedcamassaholmequation AT pingzhao anoteonthegeneralizedcamassaholmequation AT yunwu noteonthegeneralizedcamassaholmequation AT pingzhao noteonthegeneralizedcamassaholmequation |