SIAM Journal on Mathematical Analysis, Volume 53, Issue 2, Page 2567-2594, January 2021.
We consider the motion of the interface between two inviscid, incompressible, and dielectric fluids with different densities and permittivities, in the presence of a uniform electric field acting in a direction parallel to the undisturbed configuration. The system is assumed to be irrotational except the interface where the discontinuity of the tangential velocity induces vorticity. In this paper, we establish the local existence and uniqueness theory for the initial-value problem in Sobolev spaces for interfacial electrohydrodynamics. As we show, this system is locally well-posed in both two and three dimensions when surface tension is taken into account. More importantly, the tangential electric field provides a significant stabilizing effect for the two-dimensional problem (with a one-dimensional interface) such that we can prove the local-in-time well-posedness for small data even if one neglects the surface tension.

中文翻译：

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切向电场下电液界面波的适定性

SIAM数学分析杂志，第53卷，第2期，第2567-2594页，2021年1月。
我们考虑了在具有平行于不受干扰配置方向的均匀电场的情况下，具有不同密度和介电常数的两种无粘性，不可压缩和介电流体之间的界面运动。假定该系统是无旋转的，但切线速度的不连续会引起涡旋的界面除外。在本文中，我们建立了Sobolev空间中初值问题的局部存在和唯一性理论，用于界面电流体动力学。正如我们所展示的，当考虑到表面张力时，该系统在二维和三维上均处于局部良好的位置。更重要的是，