Abstract
This paper is devoted to the problem of wave propagation on a perfect conducting fluid under a vertical electric field, a kind of electrohydrodynamic waves. Three competing restoring forces resulting from gravity, surface tension, and normal electric field are taken into account. There are many numerical and experimental results on electrohydrodynamic waves, but the system’s well-posedness, which is a fundamental problem, has not been investigated in the past. We shall show the system considered is locally well posed based on energy estimates in proper Sobolev spaces and careful examinations of the Dirichlet–Neumann operators.
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