A nonlinear Schrödinger equation for the envelope of two-dimensional gravity–capillary
waves propagating at the free surface of a vertically sheared current of constant vorticity is …

We are concerned here with geophysical water waves arising as the free surface of water
flows governed by the f-plane approximation. Allowing for an arbitrary bounded …

In this paper we construct periodic capillarity–gravity water waves with an arbitrary bounded
vorticity distribution. This is achieved by re-expressing, in the height function formulation of …

We derive the dispersion relation for periodic traveling water waves propagating at the
surface of water possessing a layer of constant non-zero vorticity γ 1 adjacent to the free …

We present a variational formulation for steady periodic water waves in two-layer flows by
showing that critical points of a natural energy functional are solutions to the governing …

In this paper we consider the steady water wave problem for waves that possess a merely
L_r L r-integrable vorticity, with r ∈ (1, ∞) r∈(1,∞) being arbitrary. We first establish the …

We construct small-amplitude steady periodic gravity water waves arising as the free surface
of water flows that contain stagnation points and possess a discontinuous distribution of …

We derive the dispersion relation for water waves with surface tension and having a
piecewise constant vorticity distribution. More precisely, we consider here two scenarios; the …

In this paper, we present results about the existence and uniqueness of solutions of elliptic
equations with transmission and Wentzell boundary conditions. We provide Schauder …

In this paper, we investigate two-dimensional capillary-gravity water waves of small
amplitude, which propagate over a flat bed. We prove the existence of a local curve of …