Existence and conditional energetic stability of solitary gravitycapillary water waves with constant vorticity
(2015) In Proceedings of the Royal Society of Edinburgh. Section A 145(4). p.791883 Abstract
 We present an existence and stability theory for gravitycapillary solitary waves with constant vorticity on the surface of a body of water of finite depth. Exploiting a rotational version of the classical variational principle, we prove the existence of a minimizer of the wave energy H subject to the constraint I = 2 mu, where I is the wave momentum and 0 < mu << 1. Since H and I are both conserved quantities, a standard argument asserts the stability of the set Dmu of minimizers: solutions starting near Dmu remain close to Dmu in a suitably defined energy space over their interval of existence. In the applied mathematics literature solitary water waves of the present kind are described by solutions of a Kortewegde Vries... (More)
 We present an existence and stability theory for gravitycapillary solitary waves with constant vorticity on the surface of a body of water of finite depth. Exploiting a rotational version of the classical variational principle, we prove the existence of a minimizer of the wave energy H subject to the constraint I = 2 mu, where I is the wave momentum and 0 < mu << 1. Since H and I are both conserved quantities, a standard argument asserts the stability of the set Dmu of minimizers: solutions starting near Dmu remain close to Dmu in a suitably defined energy space over their interval of existence. In the applied mathematics literature solitary water waves of the present kind are described by solutions of a Kortewegde Vries equation (for strong surface tension) or a nonlinear Schrodinger equation (for weak surface tension). We show that the waves detected by our variational method converge (after an appropriate rescaling) to solutions of the appropriate model equation as mu down arrow 0. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/7767751
 author
 Groves, M. D. and Wahlén, Erik ^{LU}
 organization
 publishing date
 2015
 type
 Contribution to journal
 publication status
 published
 subject
 keywords
 water waves, solitary waves, vorticity, calculus of variations
 in
 Proceedings of the Royal Society of Edinburgh. Section A
 volume
 145
 issue
 4
 pages
 791  883
 publisher
 Royal Society of Edinburgh
 external identifiers

 wos:000358440200008
 scopus:84946185786
 ISSN
 03082105
 DOI
 10.1017/S0308210515000116
 language
 English
 LU publication?
 yes
 id
 9ce6fc9c51b743269b9d1afcc260ee48 (old id 7767751)
 date added to LUP
 20150909 14:05:36
 date last changed
 20180107 08:04:48
@article{9ce6fc9c51b743269b9d1afcc260ee48, abstract = {We present an existence and stability theory for gravitycapillary solitary waves with constant vorticity on the surface of a body of water of finite depth. Exploiting a rotational version of the classical variational principle, we prove the existence of a minimizer of the wave energy H subject to the constraint I = 2 mu, where I is the wave momentum and 0 < mu << 1. Since H and I are both conserved quantities, a standard argument asserts the stability of the set Dmu of minimizers: solutions starting near Dmu remain close to Dmu in a suitably defined energy space over their interval of existence. In the applied mathematics literature solitary water waves of the present kind are described by solutions of a Kortewegde Vries equation (for strong surface tension) or a nonlinear Schrodinger equation (for weak surface tension). We show that the waves detected by our variational method converge (after an appropriate rescaling) to solutions of the appropriate model equation as mu down arrow 0.}, author = {Groves, M. D. and Wahlén, Erik}, issn = {03082105}, keyword = {water waves,solitary waves,vorticity,calculus of variations}, language = {eng}, number = {4}, pages = {791883}, publisher = {Royal Society of Edinburgh}, series = {Proceedings of the Royal Society of Edinburgh. Section A}, title = {Existence and conditional energetic stability of solitary gravitycapillary water waves with constant vorticity}, url = {http://dx.doi.org/10.1017/S0308210515000116}, volume = {145}, year = {2015}, }