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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…
Nonexistence of steady waves with negative vorticity
Evgeniy Lokharu
We prove that no two-dimensional Stokes and solitary waves exist when the vorticity function is negative and the Bernoulli constant is greater than a certain critical value given e…