Diane L. Denny
We study the initial-value problem for a system of nonlinear equations that models the flow of a compressible fluid with capillary stress effects. The system includes hyperbolic equations for the density and for the velocity, and an algebraic equation (the equation of state) for the pressure. We prove the existence of a unique classical solution to an initial-value problem for this system of equations under periodic boundary conditions. The key to the proof is an a priori estimate for the density and velocity in a high Sobolev norm.
Published September 25, 2010.
Math Subject Classifications: 35A05.
Key Words: Existence; capillary; compressible fluid.
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| Diane L. Denny |
Department of Mathematics and Statistics
Texas A&M University - Corpus Christi
Corpus Christi, TX 78412, USA
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