JournalsrlmVol. 33, No. 3pp. 611–650

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

  • Massimiliano Berti

    International School for Advanced Studies (SISSA), Trieste, Italy

  • Alberto Maspero

    International School for Advanced Studies (SISSA), Trieste, Italy

  • Paolo Ventura

    International School for Advanced Studies (SISSA), Trieste, Italy
On the analyticity of the Dirichlet–Neumann operator and Stokes waves cover

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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.

Cite this article

Massimiliano Berti, Alberto Maspero, Paolo Ventura, On the analyticity of the Dirichlet–Neumann operator and Stokes waves. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 33 (2022), no. 3, pp. 611–650

DOI 10.4171/RLM/983