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

Author： Zhou Wenshu   Qin Xulong   Qu Chengyuan  

Publisher： IOP Publishing

E-ISSN： 1361-6544|28|6|1721-1743

ISSN： 0951-7715

Source： Nonlinearity, Vol.28, Iss.6, 2015-06, pp. : 1721-1743

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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) 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.

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