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 Holder regularity assumptions on their solutions.

References in corpus (1)

• Steady periodic water waves with constant vorticity: regularity and local bifurcation

Cited by in corpus (3)

• Continuous dependence on the density for stratified steady water waves
• On bounds and non-existence in the problem of steady waves with vorticity
• Equivalent formulations for steady periodic water waves of fixed mean-depth with discontinuous vorticity