Zero shear viscosity limit and boundary layer for the Navier–Stokes equations of compressible fluids between two horizontal parallel plates. (7th May 2015) - Zhou, Wenshu; Qin, Xulong; Qu, Chengyuan
Abstract: 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 ) ⩾  κ 1  ≡ 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 μ α with any α  ∈ (0, 1/2) for the boundary layer thickness.