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

Abstract

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.

References in corpus (3)

• Steady periodic water waves with constant vorticity: regularity and local bifurcation
• Capillary-gravity water waves with discontinuous vorticity: existence and regularity results
• Equivalence of weak formulations of the steady water waves equations

Cited by in corpus (1)

• Solitary water waves with discontinuous vorticity