title: Equivalence of weak formulations of the steady water waves equations.
abstract: We prove the equivalence of three weak formulations of the steady water waves equations, namely: the velocity formulation, the stream function formulation and the Dubreil-Jacotin formulation, under weak Hölder regularity assumptions on their solutions.
authors.affiliation: Department of Mathematics and Statistics, University of Reading, Whiteknights Campus, PO Box 220, Reading RG6 6AX, UK. e.varvaruca@reading.ac.uk
authors.forename: Eugen
authors.initials: E
authors.lastname: Varvaruca
authors.forename: Arghir
authors.initials: A
authors.lastname: Zarnescu