Journal article
A Lipschitz metric for the Camassa–Holm equation
- Abstract:
- We analyze stability of conservative solutions of the Cauchy problem on the line for the Camassa–Holm (CH) equation. Generically, the solutions of the CH equation develop singularities with steep gradients while preserving continuity of the solution itself. In order to obtain uniqueness, one is required to augment the equation itself by a measure that represents the associated energy, and the breakdown of the solution is associated with a complicated interplay where the measure becomes singular. The main result in this paper is the construction of a Lipschitz metric that compares two solutions of the CH equation with the respective initial data. The Lipschitz metric is based on the use of the Wasserstein metric.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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(Preview, Version of record, 1.9MB, Terms of use)
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- Publisher copy:
- 10.1017/fms.2020.22
Authors
- Publisher:
- Cambridge University Press
- Journal:
- Forum of Mathematics, Sigma More from this journal
- Volume:
- 8
- Article number:
- e27
- Publication date:
- 2020-05-21
- Acceptance date:
- 2020-04-03
- DOI:
- EISSN:
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2050-5094
- ISSN:
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2050-5094
- Language:
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English
- Keywords:
- Pubs id:
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1098921
- Local pid:
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pubs:1098921
- Deposit date:
-
2020-04-07
Terms of use
- Copyright holder:
- Carrillo et al.
- Copyright date:
- 2020
- Rights statement:
- © The Author(s) 2020 This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
- Licence:
- CC Attribution (CC BY)
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