Large-Amplitude Steady Electrohydrodynamic Solitary Waves with Constant Vorticity

Abstract

This paper investigates solitary water waves propagating along the surface of a two-dimensional dielectric fluid with constant vorticity in the presence of an external electric field. We formulate the system as a nonlinear free boundary problem where the Euler equations and electric potential equations are strongly coupled at the interface. A major challenge in such setting is the loss of standard monotonicity arguments due to the interaction between the velocity and electric fields. We overcome this difficulty by establishing new nodal properties for the combined system, ensuring the wave remains a symmetric elevation profile along the global branch. Moreover, along the global bifurcation curve, one of the following case must occur: (i) the formation of an equilibrium stagnation point, (ii) the degeneration of the conformal mapping, (iii) the onset of flow stagnation, or (iv) an unbounded increase in the dimensionless wave speed.