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Interior regularity of the compressible Navier-Stokes equations with degenerate viscosity coefficient and vacuum

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  • This paper is concerned with the interior regularity of global solutions for the one-dimensional compressible isentropic Navier-Stokes equations with degenerate viscosity coefficient and vacuum. The viscosity coefficient $\mu$ is proportional to $\rho^{\theta}$ with $0<\theta<1/3$, where $\rho$ is the density. The global existence has been established in [44] (Vong, Yang and Zhu, J. Differential Equations, 192(2), 475--501). Some ideas and more delicate estimates are introduced to prove these results.
    Mathematics Subject Classification: Primary: 35Q30, 35D10; Secondary: 76N10.

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