Upper bound on the slope of steady water waves with small adverse vorticity (Q1690312)

The authors study the upper bound on the angle of inclination of the profile of a steady 2D inviscid symmetric periodic or solitary water wave subject to gravity. Some upper bounds of the angle are known in the cases of irrotational waves and favorable vorticity. In this paper, the authors proved that the upper bound of the angle is slightly larger than \(45^\circ\), if the adverse vorticity is sufficiently small.