A Riemann-Hilbert problem and the Bernoulli boundary condition in the variational theory of Stokes waves
A Stokes wave is a steady periodic wave propagating under gravity with constant speed on the surface of an infinitely deep irrotational flow. The authors study the critical points of a certain functional in order to describe a Stokes wave, the free surface of which is characterized by the Bernoulli boundary condition. A number of properties of the solution of the associated Euler-Lagrange equation is established. Although the question as to whether for all critical points the true Bernoulli condition holds remains open, the authors show that the Bernoulli condition is always satisfied in a certain generalized sense.
scientific article; zbMATH DE number 1901026
scientific article