Commun. Math. Anal. Appl., 3 (2024), pp. 501-518.
Published online: 2024-12
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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} }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.