Global solutions of compressible Navier-Stokes equations with a density-dependent viscosity coefficient

Details Global solutions of compressible Navier-Stokes equations with a density-dependent viscosity coefficient Global solutions of compressible Navier-Stokes equations with a density-dependent viscosity coefficient

2009-04-10

arxiv.org/abs/0904.1659v1

Mathematics

Analysis of PDEs

25 pages

Scientific paper

We prove the global existence and uniqueness of the classical (weak) solution for the 2D or 3D compressible Navier-Stokes equations with a density-dependent viscosity coefficient ($\lambda=\lambda(\rho)$). Initial data and solutions are only small in the energy-norm. We also give a description of the large time behavior of the solution. Then, we study the propagation of singularities in solutions. We obtain that if there is a vacuum domain at initially, then the vacuum domain will exists for all time, and vanishes as time goes to infinity.

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