We aim at justifying rigorously different types of physically relevant diffusive limits for radiative flows. For simplicity, we consider the barotropic situation, and adopt the so-called -approximation of the radiative transfer equation. In the critical functional framework, we establish the existence of global-in-time strong solutions corresponding to small enough data, and exhibit uniform estimates with respect to the coefficients of the system. Combining with standard compactness arguments, this enables us to justify rigorously the convergence of the solutions to the expected limit systems.
Our results hold true in the whole space as well as in a periodic box with
@article{CML_2016__8_1_31_0,
author = {Rapha\"el Danchin and Bernard Ducomet},
title = {Diffusive limits for a barotropic model of radiative flow},
journal = {Confluentes Mathematici},
pages = {31--87},
publisher = {Institut Camille Jordan},
volume = {8},
number = {1},
year = {2016},
doi = {10.5802/cml.27},
language = {en},
url = {https://cml.centre-mersenne.org/articles/10.5802/cml.27/}
}
TY - JOUR AU - Raphaël Danchin AU - Bernard Ducomet TI - Diffusive limits for a barotropic model of radiative flow JO - Confluentes Mathematici PY - 2016 SP - 31 EP - 87 VL - 8 IS - 1 PB - Institut Camille Jordan UR - https://cml.centre-mersenne.org/articles/10.5802/cml.27/ DO - 10.5802/cml.27 LA - en ID - CML_2016__8_1_31_0 ER -
%0 Journal Article %A Raphaël Danchin %A Bernard Ducomet %T Diffusive limits for a barotropic model of radiative flow %J Confluentes Mathematici %D 2016 %P 31-87 %V 8 %N 1 %I Institut Camille Jordan %U https://cml.centre-mersenne.org/articles/10.5802/cml.27/ %R 10.5802/cml.27 %G en %F CML_2016__8_1_31_0
Raphaël Danchin; Bernard Ducomet. Diffusive limits for a barotropic model of radiative flow. Confluentes Mathematici, Tome 8 (2016) no. 1, pp. 31-87. doi : 10.5802/cml.27. https://cml.centre-mersenne.org/articles/10.5802/cml.27/
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