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We prove the equivalence of three weak formulations of the steady water wavesequations, namely the velocity formulation, the stream function formulation,and the Dubreil-Jacotin formulation, under weak Holder regularity assumptionson their solutions.

philosophical transactions - royal society. mathematical, physical and engineering sciences/philosophical transactions - royal society. mathematical, physical and engineering sciences

Equivalence of weak formulations of the steady water waves equations