Eighth Mississippi State - UAB Conference on Differential Equations and Computational Simulations. Electron. J. Diff. Eqns., Conference 19 (2010), pp. 45-64.

Solution to a system of equations modelling compressible fluid flow with capillary stress effects

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.

Show me the PDF file (287K), TEX file, and other files for this article.

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

Return to the table of contents for this conference.
Return to the EJDE web page