V.A. Kozlov | The subharmonic bifurcation of Stokes waves with vorticity
Channel: EIMI, PDMI RAS and Chebyshev Laboratory
Date: 2022-08-01

O.A. Ladyzhenskaya centennial conference on PDE’s, St. Petersburg, July 16 – July 22, 2022
Vladimir A. Kozlov (Linkoping University) 
The subharmonic bifurcation of Stokes waves with vorticity

My talk concerns 2D theory of steady water waves. There are two types of
waves (Stokes and solitary) studied sufficiently good. The first one is a periodic wave with exactly one crest and one through on the period. The solitary wave is described by an even function having the same limit at ±∞ and monotone to both sides from its maximum. The proof of existence of small and large water waves together with long standing Stokes conjecture about waves of highest amplitude was a result of deep study of water waves during last century. In 1980th new type of waves were discovered numerically. They are periodic and have several crests of different height on the period. They appear as a result of bifurcation when Stokes waves approach a wave of highest amplitude. Their existence was proved in the irrotational case for the channel of infinite depth by Buffoni, Dancer and Toland in 2000. In this talk I will present an existence result of subharmonic bifurcations of Stokes waves with vorticity in a channel of finite depth.