Well-posedness and blow-up solutions for an integrable nonlinearly dispersive model wave equation

Yi A. Li; Peter J. Olver

doi:10.1006/jdeq.1999.3683

Well-posedness and blow-up solutions for an integrable nonlinearly dispersive model wave equation

Yi A. Li, Peter J. Olver

Department of Mathematical Sciences

University of Minnesota Twin Cities

Research output: Contribution to journal › Article › peer-review

576 Scopus citations

Abstract

We establish local well-posedness in the Sobolev space H^s with any s>3/2 for an integrable nonlinearly dispersive wave equation arising as a model for shallow water waves known as the Camassa-Holm equation. However, unlike the more familiar Korteweg-deVries model, we demonstrate conditions on the initial data that lead to finite time blow-up of certain solutions.

Original language	English
Pages (from-to)	27-63
Number of pages	37
Journal	Journal of Differential Equations
Volume	162
Issue number	1
DOIs	https://doi.org/10.1006/jdeq.1999.3683
State	Published - 20 Mar 2000

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title = "Well-posedness and blow-up solutions for an integrable nonlinearly dispersive model wave equation",

abstract = "We establish local well-posedness in the Sobolev space Hs with any s>3/2 for an integrable nonlinearly dispersive wave equation arising as a model for shallow water waves known as the Camassa-Holm equation. However, unlike the more familiar Korteweg-deVries model, we demonstrate conditions on the initial data that lead to finite time blow-up of certain solutions.",

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AU - Li, Yi A.

AU - Olver, Peter J.

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Y1 - 2000/3/20

N2 - We establish local well-posedness in the Sobolev space Hs with any s>3/2 for an integrable nonlinearly dispersive wave equation arising as a model for shallow water waves known as the Camassa-Holm equation. However, unlike the more familiar Korteweg-deVries model, we demonstrate conditions on the initial data that lead to finite time blow-up of certain solutions.

AB - We establish local well-posedness in the Sobolev space Hs with any s>3/2 for an integrable nonlinearly dispersive wave equation arising as a model for shallow water waves known as the Camassa-Holm equation. However, unlike the more familiar Korteweg-deVries model, we demonstrate conditions on the initial data that lead to finite time blow-up of certain solutions.

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U2 - 10.1006/jdeq.1999.3683

DO - 10.1006/jdeq.1999.3683

M3 - Article

AN - SCOPUS:0034688728

SN - 0022-0396

VL - 162

SP - 27

EP - 63

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 1

ER -

Well-posedness and blow-up solutions for an integrable nonlinearly dispersive model wave equation

Abstract

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