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Zero shear viscosity limit and boundary layer for the Navier–Stokes equations of compressible fluids between two horizontal parallel plates

We consider an initial-boundary problem for the three-dimensional Navier–Stokes equations of compressible fluids between two horizontal parallel plates, where heat conductivity κ may depend on both density ρ and temperature θ such that κ(ρ, θ) ⩾ κ1 ≡ constant > 0, ∀ρ, θ > 0. We prove the global existence of strong solutions for large data and justify the zero shear viscosity limit as the shear viscosity μ goes to zero. Moreover, we establish the value μα with any α ∈ (0, 1/2) for the boundary layer thickness.