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

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

Author: Diane L. Denny (Texas A&M Univ., Corpus Christi, TX, USA)
 
Abstract: 
 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.