dc.contributor.author | Varholm, Kristoffer | |
dc.contributor.author | Wahlén, Erik | |
dc.contributor.author | Walsh, Samuel | |
dc.date.accessioned | 2020-11-03T11:18:45Z | |
dc.date.available | 2020-11-03T11:18:45Z | |
dc.date.created | 2020-11-02T09:24:12Z | |
dc.date.issued | 2020 | |
dc.identifier.citation | Communications on Pure and Applied Mathematics. 2020, 73 (12), 2634-2684. | en_US |
dc.identifier.issn | 0010-3640 | |
dc.identifier.uri | https://hdl.handle.net/11250/2686190 | |
dc.description.abstract | This paper investigates the stability of traveling wave solutions to the free boundary Euler equations with a submerged point vortex. We prove that sufficiently small‐amplitude waves with small enough vortex strength are conditionally orbitally stable. In the process of obtaining this result, we develop a quite general stability/instability theory for bound state solutions of a large class of infinite‐dimensional Hamiltonian systems in the presence of symmetry. This is in the spirit of the seminal work of Grillakis, Shatah, and Strauss (GSS) , but with hypotheses that are relaxed in a number of ways necessary for the point vortex system, and for other hydrodynamical applications more broadly. In particular, we are able to allow the Poisson map to have merely dense range, as opposed to being surjective, and to be state‐dependent.
As a second application of the general theory, we consider a family of nonlinear dispersive PDEs that includes the generalized Korteweg–de Vries (KdV) and Benjamin‐Ono equations. The stability or instability of solitary waves for these systems has been studied extensively, notably by Bona, Souganidis, and Strauss , who used a modification of the GSS method. We provide a new, more direct proof of these results, as a straightforward consequence of our abstract theory. At the same time, we allow fractional dispersion and obtain a new instability result for fractional KdV. © 2020 Wiley Periodicals, Inc. | en_US |
dc.language.iso | eng | en_US |
dc.publisher | Wiley | en_US |
dc.rights | Navngivelse 4.0 Internasjonal | * |
dc.rights.uri | http://creativecommons.org/licenses/by/4.0/deed.no | * |
dc.title | On the Stability of Solitary Water Waves with a Point Vortex | en_US |
dc.type | Journal article | en_US |
dc.type | Peer reviewed | en_US |
dc.description.version | publishedVersion | en_US |
dc.source.pagenumber | 2634-2684 | en_US |
dc.source.volume | 73 | en_US |
dc.source.journal | Communications on Pure and Applied Mathematics | en_US |
dc.source.issue | 12 | en_US |
dc.identifier.doi | https://doi.org/10.1002/cpa.21891 | |
dc.identifier.cristin | 1843988 | |
dc.relation.project | Norges forskningsråd: 231668 | en_US |
dc.relation.project | Norges forskningsråd: 250070 | en_US |
dc.description.localcode | © 2020 the Authors. Communications on Pure and Applied Mathematics is published by the Courant Institute of Mathematical Sciences and Wiley Periodicals, Inc. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. | en_US |
cristin.ispublished | true | |
cristin.fulltext | original | |
cristin.qualitycode | 2 | |