Electronic Journal of Differential Equations,
Vol. 2007(2007), No. 39, pp. 1-23.
Title: Existence and uniqueness of global solutions
to a model for the flow of an incompressible,
barotropic fluid with capillary 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 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 $L^2$ estimate for the density
$\rho$, 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.