Two-component equations modelling water waves with constant vorticity
type: Item
instance of: scholarly article
title: Two-component equations modelling water waves with constant vorticity
zbMATH Open document ID: 1353.35236
author: Joachim Escher
author: David Henry
author: B. Kolev
author: Tony Lyons
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 2016-03-02T00:00:00Z
full work available at URL: https://arxiv.org/abs/1406.1645
review text: The authors first derive a two-component system of nonlinear equations \[ m_t =\alpha u_x -au_x m -u m_x -\kappa \rho\rho_x, \quad \rho_t = -u\rho_x -(a-1)u_x\rho\text{ with }m =u-u_{xx}, \] which models two-dimensional shallow water waves with constant vorticity. Then, the authors use \textit{D. G. Ebin} and \textit{J. Marsden}'s approach [Ann. Math. (2) 92, 102--163 (1970; Zbl 0211.57401)] to prove the (local) wellposedness of this system using a geometrical framework which allows us to recast this system as a geodesic flow on an infinite-dimensional manifold. Finally, a criterion is provided which guarantees the global existence of a solution.
reviewed by: Song Jiang
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 35-02
Mathematics Subject Classification ID: 76B15
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 58D05
zbMATH DE Number: 6548058
zbMATH Keywords: water waves
zbMATH Keywords: vorticity
zbMATH Keywords: model equations
zbMATH Keywords: Euler equation
zbMATH Keywords: diffeomorphism group
MaRDI profile type: Publication
OpenAlex ID: W3106238770
arXiv ID: 1406.1645
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DOI: 10.1007/S10231-014-0461-Z
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description: scientific article; zbMATH DE number 6548058