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

TL;DR

This paper proves the analyticity of the Dirichlet-Neumann operator in unbounded domains and derives an analytic bifurcation result for Stokes waves, advancing understanding of water wave solutions in deep water.

Contribution

It establishes the analyticity of the Dirichlet-Neumann operator in infinite-depth, periodic settings and introduces an analytic bifurcation framework for Stokes waves.

Findings

Analyticity of the Dirichlet-Neumann operator in unbounded, infinite-depth domains.

Existence of analytic bifurcation for space periodic Stokes waves.

Framework for studying water waves using analytic methods.

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.