A remark on the Cauchy problem of 1D compressible Navier-Stokes equations with density-dependent viscosity coefficients

This paper is concerned with the Cauchy problems of one-dimensional compressible Navier-Stokes equations with density-dependent viscosity coefficients. By assuming ρ ₀ ∈ L ¹(R), we will prove the existence of weak solutions to the Cauchy problems for θ > 0. This will improve results in Jiu and Xin’s paper (Kinet. Relat. Models, 1(2): 313–330 (2008)) in which θ > $tfrac{1} {2} $ is required. In addition, We will study the large time asymptotic behavior of such weak solutions.