Volume 3, Issue 4
Global Solutions to the Compressible Navier-Stokes Equations for a Reacting Mixture with Temperature Dependent Transport Coefficients

Ling Wan, Tao Wang & Huijiang Zhao

Commun. Math. Anal. Appl., 3 (2024), pp. 501-518.

Published online: 2024-12

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  • 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.

  • AMS Subject Headings

76N06, 35Q35, 76N10

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COPYRIGHT: © Global Science Press

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@Article{CMAA-3-501, author = {Wan , LingWang , Tao and Zhao , Huijiang}, title = {Global Solutions to the Compressible Navier-Stokes Equations for a Reacting Mixture with Temperature Dependent Transport Coefficients}, journal = {Communications in Mathematical Analysis and Applications}, year = {2024}, volume = {3}, number = {4}, pages = {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.

}, issn = {2790-1939}, doi = {https://doi.org/10.4208/cmaa.2024-0021}, url = {http://global-sci.org/intro/article_detail/cmaa/23616.html} }
TY - JOUR T1 - Global Solutions to the Compressible Navier-Stokes Equations for a Reacting Mixture with Temperature Dependent Transport Coefficients AU - Wan , Ling AU - Wang , Tao AU - Zhao , Huijiang JO - Communications in Mathematical Analysis and Applications VL - 4 SP - 501 EP - 518 PY - 2024 DA - 2024/12 SN - 3 DO - http://doi.org/10.4208/cmaa.2024-0021 UR - https://global-sci.org/intro/article_detail/cmaa/23616.html KW - Compressible Navier-Stokes equations, reacting mixture, global large solutions, temperature dependent transport coefficients, Nishida-Smoller type result. AB -

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.

Wan , LingWang , Tao and Zhao , Huijiang. (2024). Global Solutions to the Compressible Navier-Stokes Equations for a Reacting Mixture with Temperature Dependent Transport Coefficients. Communications in Mathematical Analysis and Applications. 3 (4). 501-518. doi:10.4208/cmaa.2024-0021
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