Local well-posedness to the cauchy problem of the 3-D compressible navier-stokes equations with density-dependent viscosity

Abstract

In this article, we prove the local existence and uniqueness of the classical solution to the Cauchy problem of the 3-D compressible Navier-Stokes equations with large initial data and vacuum, if the shear viscosity μ is a positive constant and the bulk viscosity λ(ρ) = ρβ with β ≥ 0. Note that the initial data can be arbitrarily large to contain vacuum states.