Global regularity for a radiation hydrodynamics model with viscosity and thermal conductivity. (English) Zbl 1531.76078
The authors consider the system governing dynamics of astrophysical flows where gas exchanges energy with radiation. Radiation density is steady, while time derivatives of total energy, velocity, and fluid density are present in equations. The gas is ideal and polytropic. The system is in a one-dimensional periodic box. Both viscosity and thermal conductivity are taken into account. The paper aims at establishing existence of a unique global smooth non-vacuum solution for any large initial data. For a special dependence of thermal conductivity \(\kappa\) on the specific volume \(v\) and temperature \(\theta\)
\[
\kappa=\kappa_1+\kappa_2v\theta^\beta,\ \beta>13,
\]
the authors prove global existence and uniqueness of a smooth solution. The initial data must only obey the compatibility conditions, belong to the \(H^2\) space, and be positive.
Reviewer: Ilya A. Chernov (Petrozavodsk)
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 |
Keywords:
ideal polytropic gas; global existence; uniqueness; large initial data; first-order spatial derivative; dissipative estimate; pointwise estimate; compatibility conditionReferences:
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