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.

中文翻译：

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垂直电场下水动力波的适定性

本文致力于在垂直电场下在一种理想的导电流体上传播一种电液动力波的问题。考虑了重力，表面张力和法向电场引起的三个相互竞争的恢复力。关于电动液力波有许多数值和实验结果，但是该系统的适定性是一个基本问题，过去没有进行过研究。我们将根据适当的Sobolev空间中的能量估计以及对Dirichlet-Neumann算子的仔细检查，证明所考虑的系统在局部位置正确。