LAUSR

Abstract We consider a simplified compressible Navier-Stokes equations with cylindrical symmetry when viscosity coefficient λ and heat conductivity coefficient κ depend on temperature. We obtain global existence of strong solution and vanishing shear viscosity limit to the initial-boundary value problem in Eulerian coordinates. The analysis for the global existence is based on the assumption that μ = const . > 0 , 1 c ˜ θ m ≤ λ ( θ ) ≤ c ˜ ( 1 + θ m ) , κ ( θ ) = θ q , for m ∈ ( 0 , 1 ] , q ≥ m . For the part of vanishing shear viscosity limit, we require in addition that 1 c ˜ ( 1 + θ m ) ≤ λ ( θ ) ≤ c ˜ ( 1 + θ m ) . In the paper, the acceleration effect in one direction is neglected, however, we do not need any smallness assumption for the initial data.