We consider an incompressible and inviscid conducting fluid in the presence of surface tension and vertical electric field. We will reduce the system to the equations on the interface and the velocity fields. By the reduced equations, it is obtained the local-in-time estimates on the interface in $H^{3k+1}$ and the velocity fields in $H^{3k}$ by using the method introduced by Shatah and Zeng [20]. The estimates of a vertical electric field can be obtained from the estimates of the interface and elliptic estimates.

中文翻译：

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具有涡度的电动流体波的先验估计：垂直电场

在存在表面张力和垂直电场的情况下，我们考虑一种不可压缩且不粘稠的导电流体。我们将系统简化为界面和速度场上的方程。通过简化的方程，可以得到界面上的局部实时估计。$H^{3ķ+\mathrm{1个}}$ 和速度场 $H^{3ķ}$通过使用Shatah和Zeng [20]引入的方法。垂直电场的估计可以从界面的估计和椭圆估计中获得。