On the ill-posedness of the 5th-order Gardner equation
We present ill-posedness results for the initial value problem of the 5th-order Gardner equation. We use new breather solutions discovered for this higher order Gardner equation to measure the regularity of the Cauchy problem in Sobolev spaces H s ( R ) . We find the sharp Sobolev index under which...
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| Veröffentlicht in: | São Paulo Journal of Mathematical Sciences 2019-12, Vol.13 (2), p.383-390 |
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| container_end_page | 390 |
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| container_title | São Paulo Journal of Mathematical Sciences |
| container_volume | 13 |
| creator | Alejo, Miguel A. Cardoso, Eleomar |
| description | We present ill-posedness results for the initial value problem of the 5th-order Gardner equation. We use new breather solutions discovered for this higher order Gardner equation to measure the regularity of the Cauchy problem in Sobolev spaces
H
s
(
R
)
. We find the sharp Sobolev index under which the local well-posedness of the problem is lost, meaning that the dependence of 5th-order Gardner solutions upon initial data fails to be continuous. |
| doi_str_mv | 10.1007/s40863-019-00150-7 |
| format | Article |
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H
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(
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H
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(
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| fulltext | fulltext |
| identifier | ISSN: 1982-6907 |
| ispartof | São Paulo Journal of Mathematical Sciences, 2019-12, Vol.13 (2), p.383-390 |
| issn | 1982-6907 2316-9028 2306-9028 |
| language | eng |
| recordid | cdi_proquest_journals_2310413901 |
| source | SpringerLink Journals - AutoHoldings |
| subjects | Boundary value problems Cauchy problems Dependence Mathematics Mathematics and Statistics Sobolev space Special Section: Nonlinear Dispersive Equations Well posed problems |
| title | On the ill-posedness of the 5th-order Gardner equation |
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