On Global Classical Solutions to 1D Compressible Navier-Stokes Equations with Density-Dependent Viscosity and Vacuum

2018/08/09 by Lü, Boqiang, Wang, Yixuan, Wu, Yuhang
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1808.03042

Abstract

For the initial boundary value problem of compressible barotropic Navier-Stokes equations in one-dimensional bounded domains with general density-dependent viscosity and large external force, we prove that there exists a unique global classical solution with large initial data containing vacuum. Furthermore, we show that the density is bounded from above independently of time which in particular yields the large time behavior of the solution as time tends to infinity: the density and the velocity converge to the steady states in L^p and in W^1,p (1≤ p

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