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  1. Nonlinear Differential Equations and Applications NoDEA
  2. Nonlinear Differential Equations and Applications NoDEA : Volume 20
  3. Nonlinear Differential Equations and Applications NoDEA : Volume 20, Issue 5, October 2013
  4. On the stability of travelling waves with vorticity obtained by minimization
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Nonlinear Differential Equations and Applications NoDEA : Volume 23
Nonlinear Differential Equations and Applications NoDEA : Volume 22
Nonlinear Differential Equations and Applications NoDEA : Volume 21
Nonlinear Differential Equations and Applications NoDEA : Volume 20
Nonlinear Differential Equations and Applications NoDEA : Volume 20, Issue 6, December 2013
Nonlinear Differential Equations and Applications NoDEA : Volume 20, Issue 5, October 2013
Periodic solutions in general scalar non-autonomous models with delays
On the stability of travelling waves with vorticity obtained by minimization
A two-gradient approach for phase transitions in thin films
A priori estimates for a class of degenerate elliptic equations
P-Laplacian problems with nonlinearities interacting with the spectrum
Nonlinear Differential Equations and Applications NoDEA : Volume 20, Issue 4, August 2013
Nonlinear Differential Equations and Applications NoDEA : Volume 20, Issue 3, June 2013
Nonlinear Differential Equations and Applications NoDEA : Volume 20, Issue 2, April 2013
Nonlinear Differential Equations and Applications NoDEA : Volume 20, Issue 1, February 2013
Nonlinear Differential Equations and Applications NoDEA : Volume 19
Nonlinear Differential Equations and Applications NoDEA : Volume 18
Nonlinear Differential Equations and Applications NoDEA : Volume 17
Nonlinear Differential Equations and Applications NoDEA : Volume 16
Nonlinear Differential Equations and Applications NoDEA : Volume 15
Nonlinear Differential Equations and Applications NoDEA : Volume 14
Nonlinear Differential Equations and Applications NoDEA : Volume 13
Nonlinear Differential Equations and Applications NoDEA : Volume 12
Nonlinear Differential Equations and Applications NoDEA : Volume 11
Nonlinear Differential Equations and Applications NoDEA : Volume 10
Nonlinear Differential Equations and Applications NoDEA : Volume 9
Nonlinear Differential Equations and Applications NoDEA : Volume 8
Nonlinear Differential Equations and Applications NoDEA : Volume 7
Nonlinear Differential Equations and Applications NoDEA : Volume 6
Nonlinear Differential Equations and Applications NoDEA : Volume 5
Nonlinear Differential Equations and Applications NoDEA : Volume 4

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On the stability of travelling waves with vorticity obtained by minimization

Content Provider SpringerLink
Author Buffoni, B. Burton, G. R.
Copyright Year 2013
Abstract We modify the approach of Burton and Toland Comm. Pure Appl. Math. LXIV. 975–1007 (2011) to show the existence of periodic surface water waves with vorticity in order that it becomes suited to a stability analysis. This is achieved by enlarging the function space to a class of stream functions that do not correspond necessarily to travelling profiles. In particular, for smooth profiles and smooth stream functions, the normal component of the velocity field at the free boundary is not required a priori to vanish in some Galilean coordinate system. Travelling periodic waves are obtained by a direct minimization of a functional that corresponds to the total energy and that is therefore preserved by the time-dependent evolutionary problem (this minimization appears in Comm. Pure Appl. Math. LXIV. 975–1007 2011 after a first maximization). In addition, we not only use the circulation along the upper boundary as a constraint, but also the total horizontal impulse (the velocity becoming a Lagrange multiplier). This allows us to preclude parallel flows by choosing appropriately the values of these two constraints and the sign of the vorticity. By stability, we mean conditional energetic stability of the set of minimizers as a whole, the perturbations being spatially periodic of given period. Our proofs depend on the assumption that the surface offers some resistance to stretching and bending.
Ending Page 1629
Page Count 33
Starting Page 1597
File Format PDF
ISSN 10219722
e-ISSN 14209004
Journal Nonlinear Differential Equations and Applications NoDEA
Issue Number 5
Volume Number 20
Language English
Publisher Springer Basel
Publisher Date 2013-03-19
Publisher Place Basel
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword Methods involving semicontinuity and convergence; relaxation Hydrodynamic stability Stability and instability of nonparallel flows PDEs in connection with fluid mechanics Analysis Vorticity Vortex flows Surface wave Energy minimization Rearrangement Water waves, gravity waves; dispersion and scattering, nonlinear interaction
Content Type Text
Resource Type Article
Subject Applied Mathematics Analysis
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