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.