1 research outputs found
Global Solution for Gas-Liquid Flow of 1-D van der Waals Equation of State with Large Initial Data
This paper is concerned with a diffuse interface model for the gas-liquid
phase transition. The model consists the compressible Navier-Stokes equations
with van der Waals equation of state and a modified Allen-Cahn equation. The
global existence and uniqueness of strong solution with the periodic boundary
condition (or the mixed boundary condition) in one dimensional space is proved
for large initial data. Furthermore, the phase variable and the density of the
gas-liquid mixture are proved to stay in the physical reasonable interval. The
proofs are based on the elementary energy method and the maximum principle, but
with new development, where some techniques are introduced to establish the
uniform bounds of the density and to treat the non-convexity of the pressure
function