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

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  • 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.

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