Abstract
We are concerned with global existence and uniqueness of strong solutions for a general model of viscous and heat-conductive gases. The initial data are supposed to be close to a stable equilibrium with constant density and temperature. Using uniform estimates for the linearized system with a convection term, we get global well-posedness in a functional setting invariant with respect to the scaling of the associated equations (in space dimension N≧3). We also show a smoothing effect on the velocity and the temperature, and a decay on the difference between the density and the constant reference state. These results extend a previous paper devoted to the barotropic case (see [5]).
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Accepted March 30, 2001¶Published online September 3, 2001
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Danchin, R. Global Existence in Critical Spaces¶for Flows of Compressible¶Viscous and Heat-Conductive Gases. Arch. Rational Mech. Anal. 160, 1–39 (2001). https://doi.org/10.1007/s002050100155
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DOI: https://doi.org/10.1007/s002050100155