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2008, Volume 7, Issue 2: 373-381. Doi: 10.3934/cpaa.2008.7.373
This issue Previous Article Multiple solutions for a class of Ambrosetti-Prodi type problems for systems involving critical Sobolev exponents Next Article On semilinear elliptic equations involving critical Sobolev exponents and sign-changing weight function

One dimensional compressible Navier-Stokes equations with density-dependent viscosity and free boundaries

  • 1.

    Department of Mathematics, Sun Yat-Sen University, Guangzhou, 510275

  • 2.

    Department of Mathematics, Sun Yat-sen University, Guangzhou 510275

  • 3.

    Department of Mathematics, College of Mathematics and Information Science, GuangZhou University, Guangzhou, 510006

Received:  July 2006
Revised:  December 2007
Published:  March 2008
Abstract / Introduction Related Papers Cited by
    Abstract
  • A free-boundary problem is studied for the one-dimensional compressible Navier-Stokes equations with density-dependent viscosity that decreases (to zero) with decreasing density, i.e., $\mu=A\rho^\theta$, where $A$ and $\theta$ are positive constants. The existence and uniqueness of the global weak solutions are obtained with $\theta\in (0,1]$, which improves the previous results and no vacuum is developed in the solutions in a finite time provided the initial data does not contain vacuum.
    Mathematics Subject Classification: Primary: 35Q30, 76N10; Secondary: 76N15.

    Citation:
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