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

2022/01/12 by Berti, Massimiliano, Maspero, Alberto, Ventura, Paolo
#35B32 #35J05 #76B15 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2201.04675

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.

Related

• Stokes waves with vorticity
• Stokes Waves in Water of Finite Depth
• Cauchy theory for the water waves system in an analytic framework
• Analyticity and Stable Computation of Dirichlet-Neumann Operators for Laplace's Equation under Quasiperiodic Boundary Conditions in Two and Three Dimensions
• Steady periodic water waves under nonlinear elastic membranes