Bounds for water waves (Q1097781): Difference between revisions

This paper presents a fairly sharp bound for solutions to Nekrasov's equation [\textit{A. I. Nekrasov}: On steady waves. Izv. Ivanovo-Voznesensk. Politekhn. 3, 52-65 (1921)]. This equation arises from the following physical situation: consider two-dimensional waves on the surface of an incompressible, inviscid fluid acted upon by gravity. The flow is to be irrotational, and the waves move from left to right without change of form and with a constant velocity. By transforming to a moving coordinate system, the flow becomes steady and Bernoulli's Theorem holds. If the effect of surface tension is neglected, then the pressure will be constant on the (unknown) free surface.