The existence of global weak solutions for a weakly dissipative Camassa-Holm equation in H1(R)
The existence of global weak solutions to the Cauchy problem for a weakly dissipative Camassa-Holm equation is established in the space C([0,∞)×R)nL∞([0,∞);H1(R)) under the assumption that the initial value u 0 (x) only belongs to the space H 1 (R) . The limit of viscous approximations, a one-sided...
| Main Authors: | , , |
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| Format: | Journal Article |
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SpringerOpen
2013
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| Online Access: | http://hdl.handle.net/20.500.11937/11326 |
| _version_ | 1848747775756337152 |
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| author | Lai, S. Li, N. Wu, Yong Hong |
| author_facet | Lai, S. Li, N. Wu, Yong Hong |
| author_sort | Lai, S. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | The existence of global weak solutions to the Cauchy problem for a weakly dissipative Camassa-Holm equation is established in the space C([0,∞)×R)nL∞([0,∞);H1(R)) under the assumption that the initial value u 0 (x) only belongs to the space H 1 (R) . The limit of viscous approximations, a one-sided super bound estimate and a space-time higher-norm estimate for the equation are established to prove the existence of the global weak solution. |
| first_indexed | 2025-11-14T06:54:31Z |
| format | Journal Article |
| id | curtin-20.500.11937-11326 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T06:54:31Z |
| publishDate | 2013 |
| publisher | SpringerOpen |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-113262017-09-13T14:53:18Z The existence of global weak solutions for a weakly dissipative Camassa-Holm equation in H1(R) Lai, S. Li, N. Wu, Yong Hong global weak solution Camassa-Holm type equation existence The existence of global weak solutions to the Cauchy problem for a weakly dissipative Camassa-Holm equation is established in the space C([0,∞)×R)nL∞([0,∞);H1(R)) under the assumption that the initial value u 0 (x) only belongs to the space H 1 (R) . The limit of viscous approximations, a one-sided super bound estimate and a space-time higher-norm estimate for the equation are established to prove the existence of the global weak solution. 2013 Journal Article http://hdl.handle.net/20.500.11937/11326 10.1186/1687-2770-2013-26 SpringerOpen fulltext |
| spellingShingle | global weak solution Camassa-Holm type equation existence Lai, S. Li, N. Wu, Yong Hong The existence of global weak solutions for a weakly dissipative Camassa-Holm equation in H1(R) |
| title | The existence of global weak solutions for a weakly dissipative Camassa-Holm equation in H1(R) |
| title_full | The existence of global weak solutions for a weakly dissipative Camassa-Holm equation in H1(R) |
| title_fullStr | The existence of global weak solutions for a weakly dissipative Camassa-Holm equation in H1(R) |
| title_full_unstemmed | The existence of global weak solutions for a weakly dissipative Camassa-Holm equation in H1(R) |
| title_short | The existence of global weak solutions for a weakly dissipative Camassa-Holm equation in H1(R) |
| title_sort | existence of global weak solutions for a weakly dissipative camassa-holm equation in h1(r) |
| topic | global weak solution Camassa-Holm type equation existence |
| url | http://hdl.handle.net/20.500.11937/11326 |