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Global Solutions to the Compressible Navier-Stokes Equations for a Reacting Mixture with Temperature Dependent Transport Coefficients

Global Solutions to the Compressible Navier-Stokes Equations for a Reacting Mixture with Temperature Dependent Transport Coefficients

Year:    2024

Author:    Ling Wan, Tao Wang, Huijiang Zhao

Communications in Mathematical Analysis and Applications, Vol. 3 (2024), Iss. 4 : pp. 501–518

Abstract

We consider the compressible Navier-Stokes equations for a reacting ideal polytropic gas when the coefficients of viscosity, thermal conductivity, and species diffusion are general smooth functions of temperature. The choice of temperature-dependent transport coefficients is motivated by the kinetic theory and experimental results. We establish the existence, uniqueness, and time-asymptotic behavior of global solutions for one-dimensional, spherically symmetric, or cylindrically symmetric flows under certain assumptions on the $H^2$ norm of the initial data. This is a Nishida-Smoller type global solvability result, since the initial perturbations can be large if the adiabatic exponent is close to 1.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cmaa.2024-0021

Communications in Mathematical Analysis and Applications, Vol. 3 (2024), Iss. 4 : pp. 501–518

Published online:    2024-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    18

Keywords:    Compressible Navier-Stokes equations reacting mixture global large solutions temperature dependent transport coefficients Nishida-Smoller type result.

Author Details

Ling Wan

Tao Wang

Huijiang Zhao