On a variational approach for Stokes conjecture in water waves: existence of regular waves

Danut Arama Department of Mathematical Sciences Carnegie Mellon University Pittsburgh, PA 15213, USA darama@andrew.cmu.edu

Giovanni Leoni Department of Mathematical Sciences Carnegie Mellon University Pittsburgh, PA 15213, USA giovanni@andrew.cmu.edu

Abstract: Using the variational approach of Alt and Caffarelli in this paper we give an alternative proof of a theorem of Keady and Norbury on the existence of a family of regular water waves.