Electron. J. Diff. Eqns., Vol. 2007(2007), No. 39, pp. 1-23.

Existence and uniqueness of global solutions to a model for the flow of an incompressible, barotropic fluid with capillary effects

Diane L. Denny

We study the initial-value problem for a system of nonlinear equations that models the flow of an inviscid, incompressible, barotropic fluid with capillary stress effects. We prove the global-in-time existence of a unique, classical solution to this system of equations, with a small initial velocity gradient. The key to the proof lies in using an $L^2$ estimate for the density $\rho$, and using the smallness of the initial velocity gradient, to obtain uniqueness for the density.

Submitted August 10, 2006. Published March 6, 2007.
Math Subject Classifications: 35A05.
Key Words: Existence; uniqueness; capillary; incompressible; inviscid fluid.

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Diane Denny
Department of Mathematics and Statistics
Texas A&M University - Corpus Christi
Corpus Christi, TX 78412, USA
email: diane.denny@tamucc.edu

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