SOLUTIONS FOR A MODEL OF LOW-SPEED FLOW FOR FLUIDS WITH CAPILLARY EFFECTS

We study the initial-value problem for a system of equations that models the low-speed flow of an inviscid, incompressible fluid with capillary stress effects. The system includes hyperbolic equations for the density and velocity, a parabolic equation for the temperature, and an algebraic equation (the equation of state). We prove the local existence of a unique, classical solution to an initial-value problem with suitable initial data. We also present a new, a priori estimate for the density, and then use this estimate, along with a bootstrapping argument, to show that if the regularity of the initial data for the temperature and velocity (but not the density) is increased, then the regularity of the solution for the density, temperature, and velocity may be increased.