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...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/404781 |
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| Summary: | 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. |
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| ISSN: | 1085-3375 1687-0409 |