On a simplified compressible Navier-Stokes equations with temperature-dependent viscosity

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 E...

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Bibliographic Details
Published in:Journal of Differential Equations 2020-02, Vol.268 (5), p.1974-2011
Main Authors: Wen, Huanyao, Zhao, Xinhua
Format: Article
Language:English
Subjects:
Compressible Navier-Stokes equations
Global strong solutions
Temperature-dependent heat conductivity
Temperature-dependent viscosity
Vanishing shear viscosity limit
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Summary: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.>0,1c˜θm≤λ(θ)≤c˜(1+θm),κ(θ)=θq, for m∈(0,1],q≥m. For the part of vanishing shear viscosity limit, we require in addition that 1c˜(1+θm)≤λ(θ)≤c˜(1+θm). In the paper, the acceleration effect in one direction is neglected, however, we do not need any smallness assumption for the initial data.
ISSN:0022-0396
1090-2732
DOI:10.1016/j.jde.2019.09.023