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• W2265383893 abstract "In this paper we derive a new formulation of the water waves equations with vorticity that generalizes the well-known Zalkarov-Craig-Sulem formulation used in the irrotational case. We prove the local well-posedness of this formulation, and show that it is formally Hamiltonian. This new for- mulation is cast in Eulerian variable, and in finite depth; we show that it can be used to provide uniform bounds on the lifespan and on the norms of the solutions in the singular shallow water regime. As an application to these re- sults, we derive and provide the first rigorous justification of a shallow water model for water waves in presence of vorticity; we show in particular that a third equation must be added to the standard model to recover the velocity at the surface from the averaged velocity." @default.
• W2265383893 created "2016-06-24" @default.
• W2265383893 creator A5062942463 @default.
• W2265383893 creator A5077625788 @default.
• W2265383893 date "2014-02-03" @default.
• W2265383893 modified "2023-09-27" @default.
• W2265383893 title "Well-posedness and shallow-water stability for a new Hamiltonian formulation of the water waves equations with vorticity" @default.
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• W2265383893 hasPublicationYear "2014" @default.
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