A priori estimates of the electrohydrodynamic waves with vorticity: horizontal electric field

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.

KEYWORDS:

• Electrohydrodynamic waves
• horizontal electric field
• vorticity

2010 MR SUBJECT CLASSIFICATIONS:

• 35Q31
• 35R35
• 76W05

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

Jiaqi Yang was supported by NSFC [grant number 12001429] and the Fundamental Research Funds for the Central Universities [grant number G2020KY05205].