On the analyticity of the Dirichlet–Neumann operator and Stokes waves

Abstract

We prove an analyticity result for the Dirichlet-Neumann operator under space periodic boundary conditions in any dimension in an unbounded domain with infinite depth. We derive an analytic bifurcation result of analytic Stokes waves –i.e. space periodic traveling solutions– of the water waves equations in deep water. MSC 2020: 76B15, 35B32, 35J05.