Navier-Stokes equations with degenerate viscosity, vacuum and gravitational force

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Original languageEnglish
Pages (from-to)347-374
Journal / PublicationMathematical Methods in the Applied Sciences
Issue number3
Publication statusPublished - Feb 2007


The global existence of weak solutions to the compressible Navier-Stokes equations with vacuum attracts many research interests nowadays. For the isentropic gas, the viscosity coefficient depends on density function from physical point of view. When the density function connects to vacuum continuously, the vacuum degeneracy gives some analytic difficulties in proving global existence. In this paper, we consider this case with gravitational force and fixed boundary condition. By giving a series of a priori estimates on the solution coping with the degeneracy of vacuum, gravitational force and boundary effect, we give global existence and uniqueness results similar to the case without force and boundary. Copyright © 2006 John Wiley & Sons, Ltd.

Research Area(s)

  • A priori estimates, Global existence, Navier-Stokes equations, Vacuum