Formation of singularities at the interface of liquid dielectrics in a horizontal electric field in the presence of tangential velocity discontinuity

Nonlinear dynamics of the interface of dielectric liquids under the conditions of suppression of the Kelvin–Helmholz instability by a tangential electric field has been investigated. Two broad classes of exact analytical solutions to the equations of motion describing the evolution of spatially localized and periodic interface perturbations have been found. Both classes of solutions tend to the formation of strong singularities: interface discontinuities with formally infinite amplitudes. The discontinuity sign is determined by the sign of liquid velocity jump at the interface.