Zero shear viscosity limit and boundary layer for the Navier–Stokes equations of compressible fluids between two horizontal parallel plates. (7th May 2015)

• Record Type: Journal Article
• Authors: Zhou, Wenshu; Qin, Xulong; Qu, Chengyuan
• Is Part Of: Nonlinearity. Volume 28:Number 6(2015:Jun.)
• Page Start: 1721
• Page End: 1743
• Publication Date: 2015-05-07
• Subjects: Navier–Stokes equations -- global existence -- zero shear viscosity -- convergence rate -- boundary layer; 35Q30 -- 35D35 -- 76N10 -- 35B45 -- 35B40 -- 76N20.; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/0951-7715/28/6/1721
• Languages: English
• ISSNs: 0951-7715

Abstract

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.