A note on compressible Navier–Stokes equations with vacuum state in one dimension Original Research Article

In this note, we obtain an uniqueness result for the one-dimensional compressible Navier–Stokes equations for isentropic flow connecting to vacuum state with a continuous density when viscosity coefficient μ is proportional to ρθ and 0<θ<1/2, where ρ is the density. The global existence of weak solutions has been solved in (Commun. Pure Appl. Anal. preprint, 2004). Furthermore, we improve the uniqueness result obtained in (J. Differential Equations 192 (2003) 475) to the large interval 0<θ<1/3.