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Global existence of smooth solutions for the diffusion approximation model of general gas in radiation hydrodynamics. (English) Zbl 07762007

The authors consider the 3D diffusion approximation model in radiation thermodynamics. The governing equations are conservation laws for density, velocity, temperature of the fluid and for the radiation. The equation for the latter is of diffusion type, with black-body emitting source and linear sink due to absorption. Initial data have finite positive limits at infinity (as \(|x|\to\infty\)). The gas state is more general than the ideal polytropic gas. The authors prove global existence of the unique solution to the Cauchy problem in a Sobolev space. The decay rate is estimated as well.

MSC:

76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
35Q35 PDEs in connection with fluid mechanics
78A40 Waves and radiation in optics and electromagnetic theory
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