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Global Weak Solutions to the 1D Compressible Navier-Stokes Equations with Radiation

Commun. Math. Anal.
Volume 8, Number 3 (2010), 23 - 65

Global Weak Solutions to the 1D Compressible Navier-Stokes Equations with Radiation

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Abstract

We consider an initial-boundary value problem for the equations of one-dimensional motions of a compressible viscous heat-conducting gas coupled with radiation through a radiative transfer equation. Assuming suitable hypotheses on the transport coefficients, we prove that the problem admits a unique weak solution.