Benjamin-Ono Kadomtsev-Petviashvili’s models in interfacial electro-hydrodynamics. (English) Zbl 1408.76579
Summary: Three-dimensional nonlinear potential free surface flows in the presence of vertical electric fields are considered. Both the effects of gravity and surface tension are included in the dynamic boundary condition. An asymptotic analysis (based on the assumptions of small depth and small free surface displacements) is presented. It is shown that the problem can be modelled by a Benjamin-Ono Kadomtsev-Petviashvili equation. Furthermore a fifth order Benjamin-Ono Kadomtsev-Petviashvili equation is derived to describe the flows in the particular case of values of the Bond number close to 1/3.
MSC:
| 76W05 | Magnetohydrodynamics and electrohydrodynamics |
| 76B15 | Water waves, gravity waves; dispersion and scattering, nonlinear interaction |
| 76B25 | Solitary waves for incompressible inviscid fluids |
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