Abstract
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 H3k+1 and the velocity fields in H3k 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.
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