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On negative eigenvalues of the spectral problem for water waves of highest amplitude
Vladimir Kozlov, Evgeniy Lokharu
We consider a spectral problem associated with steady water waves of extreme form on the free surface of a rotational flow. It is proved that the spectrum of this problem contains…
An asymptotic behaviour near the crest of waves of extreme form on water of finite depth
Vladimir Kozlov, Evgeniy Lokharu
We prove local higher-order asymptotics for extreme water waves with vorticity near stagnation points. We obtain that the behaviour of solutions and their regularity depend substan…
A sharp version of the Benjamin and Lighthill conjecture for steady waves with vorticity
Evgeniy Lokharu
We prove the Benjamin and Lighthill conjecture for all two-dimensional steady water waves with an arbitrary vorticity distribution. We show that the flow force constant of an arbit…
Global bifurcation and highest waves on water of finite depth
Vladimir Kozlov, Evgeniy Lokharu
We consider the two-dimensional problem for steady water waves with vorticity on water of finite depth. While neglecting the effects of surface tension we construct connected famil…
Improved bound in the Benjamin and Lighthill conjecture
Evgeniy Lokharu
The classical Benjamin and Lighthill conjecture about steady water waves states that the non-dimensional flow force constant of a solution is bounded by the corresponding constants…
An existence theory for small-amplitude doubly periodic water waves with vorticity
Evgeniy Lokharu, Douglas Svensson Seth, Erik Wahlén
We prove the existence of three-dimensional steady gravity-capillary waves with vorticity on water of finite depth. The waves are periodic with respect to a given two-dimensional l…