Sastre Gómez, Silvia2022-10-312022-10-312017-05-05Sastre Gómez, S. (2017). Equivalent formulations for steady periodic water waves of fixed mean-depth with discontinuous vorticity. Discrete and continuous dynamical systems. Series A, 37 (5), 2669-2680. https://doi.org/10.3934/dcds.2017114.1078-09471553-5231https://hdl.handle.net/11441/138511In 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.application/pdf11 p.engAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Water wavesdiscontinuous vorticityfixed-depth flowsHölder spacesweak solutioninfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccesshttps://doi.org/10.3934/dcds.2017114