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 estimate for the density , 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
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