The Cauchy Problem for a Fifth-Order Dispersive Equation
This paper is devoted to studying the Cauchy problem for a fifth-order equation. We prove that it is locally well-posed for the initial data in the Sobolev space Hs(R) with s≥1/4. We also establish the ill-posedness for the initial data in Hs(R) with s<1/4. Thus, the regularity requirement for th...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/404781 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832563346739560448 |
|---|---|
| author | Hongjun Wang Yongqi Liu Yongqiang Chen |
| author_facet | Hongjun Wang Yongqi Liu Yongqiang Chen |
| author_sort | Hongjun Wang |
| collection | DOAJ |
| description | This paper is devoted to studying the Cauchy problem for a fifth-order
equation. We prove that it is locally well-posed for the initial data in the Sobolev
space Hs(R) with s≥1/4. We also establish the ill-posedness for the initial data in
Hs(R) with s<1/4. Thus, the regularity requirement for the fifth-order dispersive equations s≥1/4 is sharp. |
| format | Article |
| id | doaj-art-2a74ee568bdf49d5ba271c2f174dad65 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-2a74ee568bdf49d5ba271c2f174dad652025-02-03T01:20:24ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/404781404781The Cauchy Problem for a Fifth-Order Dispersive EquationHongjun Wang0Yongqi Liu1Yongqiang Chen2College of Mathematics and Information Science, Henan Normal University, Xinxiang, Henan 453007, ChinaCollege of Mathematics and Information Science, Henan Normal University, Xinxiang, Henan 453007, ChinaCollege of Mathematics and Information Science, Henan Normal University, Xinxiang, Henan 453007, ChinaThis paper is devoted to studying the Cauchy problem for a fifth-order equation. We prove that it is locally well-posed for the initial data in the Sobolev space Hs(R) with s≥1/4. We also establish the ill-posedness for the initial data in Hs(R) with s<1/4. Thus, the regularity requirement for the fifth-order dispersive equations s≥1/4 is sharp.http://dx.doi.org/10.1155/2014/404781 |
| spellingShingle | Hongjun Wang Yongqi Liu Yongqiang Chen The Cauchy Problem for a Fifth-Order Dispersive Equation Abstract and Applied Analysis |
| title | The Cauchy Problem for a Fifth-Order Dispersive Equation |
| title_full | The Cauchy Problem for a Fifth-Order Dispersive Equation |
| title_fullStr | The Cauchy Problem for a Fifth-Order Dispersive Equation |
| title_full_unstemmed | The Cauchy Problem for a Fifth-Order Dispersive Equation |
| title_short | The Cauchy Problem for a Fifth-Order Dispersive Equation |
| title_sort | cauchy problem for a fifth order dispersive equation |
| url | http://dx.doi.org/10.1155/2014/404781 |
| work_keys_str_mv | AT hongjunwang thecauchyproblemforafifthorderdispersiveequation AT yongqiliu thecauchyproblemforafifthorderdispersiveequation AT yongqiangchen thecauchyproblemforafifthorderdispersiveequation AT hongjunwang cauchyproblemforafifthorderdispersiveequation AT yongqiliu cauchyproblemforafifthorderdispersiveequation AT yongqiangchen cauchyproblemforafifthorderdispersiveequation |