Diffusive limits for a barotropic model of radiative flow
Confluentes Mathematici, Tome 8 (2016) no. 1, pp. 31-87.

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 P1-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 n as well as in a periodic box 𝕋 n with n2.

Reçu le : 2015-08-09
Révisé le : 2016-07-01
Accepté le : 2016-07-01
Publié le : 2016-09-28
DOI : https://doi.org/10.5802/cml.27
Classification : 35Q35,  35A01,  35B25,  35D35,  76N10
Mots clés: Radiation hydrodynamics, Navier-Stokes system, diffusive limit, critical regularity, P1-approximation
@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 = {cml.centre-mersenne.org/item/CML_2016__8_1_31_0/}
}
Danchin, Raphaël; Ducomet, Bernard. 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/item/CML_2016__8_1_31_0/

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