Electron. J. Diff. Eqns., Vol. 2008(2008), No. 93, pp. 1-9.

Analytic solution of an initial-value problem from Stokes flow with free boundary

Xuming Xie

We study an initial-value problem arising from Stokes flow with free boundary. If the initial data is analytic in disk $\mathcal{R}_r$ containing the unit disk, it is proved that unique solution, which is analytic in $\mathcal{R}_s$ for $s\in (1,r)$, exists locally in time.

Submitted March 5, 2008. Published July 2, 2008.
Math Subject Classifications: 35Q72, 74F05, 80A22.
Key Words: Stokes flow; free boundary problem; analytic solution; abstract Cauchy-Kovalevsky problem; initial-value problem.

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Xuming Xie
Department of Mathematics, Morgan State University
Baltimore, MD 21251, USA
email: xuming.xie@morgan.edu

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