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May  2017, 37(5): 2669-2680. doi: 10.3934/dcds.2017114

## Equivalent formulations for steady periodic water waves of fixed mean-depth with discontinuous vorticity

 Departamento de Matemática, Universidade Federal de Pernambuco, Av. Jornalista Aníbal Fernandes, Recife, Pernambuco, Brazil

*The author is supported by Science Foundation Ireland (SFI) under the grant 13/CDA/2117

Received  June 2016 Revised  December 2016 Published  February 2017

Fund Project: The author is supported by Science Foundation Ireland (SFI) under the grant 13/CDA/2117.

In this work we prove the equivalence between three different weak formulations of the steady periodic water wave problem where the vorticity is discontinuous. In particular, we prove that generalised versions of the standard Euler and stream function formulation of the governing equations are equivalent to a weak version of the recently introduced modified-height formulation. The weak solutions of these formulations are considered in Hölder spaces.

Citation: Silvia Sastre-Gomez. Equivalent formulations for steady periodic water waves of fixed mean-depth with discontinuous vorticity. Discrete & Continuous Dynamical Systems - A, 2017, 37 (5) : 2669-2680. doi: 10.3934/dcds.2017114
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