ABSTRACT

In this paper, we are concerned with an incompressible and inviscid conducting fluid in the presence of surface tension and horizontal electric field. It is obtained the local-in-time estimates on the interface in $H^{\left(3/2\right)k+1}$ and the velocity fields in $H^{\left(3/2\right)k}$ by using the method introduced by Shatah and Zeng [A priori estimates for fluid interface problems. Commun Pure Appl Math. 2008;61(6):848–876]. The estimates of a horizontal electric field can be obtained from the estimates of the interface and elliptic estimates.

中文翻译：

---

具有涡量的电流体动力波的先验估计：水平电场

摘要

在本文中，我们关注存在表面张力和水平电场的不可压缩和无粘性导电流体。它是在接口上获得的本地时间估计$H^{\left(\mathrm{3个}/\mathrm{2个}\right)k+\mathrm{1个}}$和速度场$H^{\left(\mathrm{3个}/\mathrm{2个}\right)k}$通过使用 Shatah 和 Zeng 介绍的方法 [流体界面问题的先验估计。Commun 纯应用数学。2008;61(6):848-876]。水平电场的估计可以从界面估计和椭圆估计中获得。