IJPAM: Volume 45, No. 2 (2008)

COMPRESSIBLE FLOWS WITH NON-VANISHING
SURFACE TENSION AND DENSITY-DEPENDENT VISCOSITY

Gabriele Witterstein
Center for Mathematical Sciences
Munich University of Technology
3, Boltzmannstrasse, Garching by Munich, D-85747, GERMANY
e-mail: gw@ma.tum.de


Abstract.We consider a free boundary problem of the one-dimensional, compressible Navier-Stokes equations for an isothermal flow coupled with an Allen-Cahn equation modeling a phase transition of a medium. The medium is connecting to a vacuum state with a jump in the density. Here we consider density-dependent viscosity $\mu=\rho^\theta$ and a density-dependent transition layer. We prove that there exists an unique, weak solution globally in time, provided that $\theta<1/2$.

Received: April 10, 2008

AMS Subject Classification: 35Q30, 76T30, 82B26

Key Words and Phrases: compressible Navier-Stokes equations, phase transition, variable transition layer, modeling biomaterials

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 45
Issue: 2