Vacuum states on compressible Navier-Stokes equations with general density-dependent viscosity and general pressure law. (English) Zbl 1134.35389
Summary: We study the one-dimensional motion of viscous gas with a general pressure law and a general density-dependent viscosity coefficient when the initial density connects to the vacuum state with a jump. We prove the global existence and the uniqueness of weak solutions to the compressible Navier-Stokes equations by using the line method. For this, some new a priori estimates are obtained to take care of the general viscosity coefficient \(\mu (\rho )\) instead of \(\rho ^{ \theta }\).
MSC:
| 35Q30 | Navier-Stokes equations |
| 76N10 | Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics |
| 35B45 | A priori estimates in context of PDEs |
| 35D30 | Weak solutions to PDEs |
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