Non-equilibrium-diffusion limit of the compressible magnetohydrodynamic radiation model

Lei Li; Zhengce Zhang

doi:10.3934/dcdsb.2025055

Article Contents

2025, Volume 30, Issue 10: 3882-3909. Doi: 10.3934/dcdsb.2025055

This issue Previous Article Optimal decay of the magnetohydrodynamic model for quantum plasmas with potential force Next Article Statistical inference for ergodic diffusion with Markovian switching

Non-equilibrium-diffusion limit of the compressible magnetohydrodynamic radiation model

Lei Li^1, and
Zhengce Zhang^1, ,

1.
School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049, China

^*Corresponding author: Zhengce Zhang
^*Corresponding author: Zhengce Zhang

Received: April 2024

Revised: March 2025

Early access: April 10, 2025

Published online: April 10, 2025

The corresponding author is supported by [NSFC grants 12271423 and 12071044], and the Shaanxi Fundamental Science Research Project for Mathematics and Physics [23JSY026].

Abstract / Introduction Full Text(HTML) Related Papers Cited by

Abstract

We rigorously justify the non-equilibrium-diffusion limit of the compressible magnetohydrodynamics model coupled with a radiative transfer equation arising in radiation magnetohydrodynamics. For general initial data, we establish the uniform existence of solutions to the coupled model in $ \mathbb{T}^{3} $ or $ \mathbb{R}^{3} $ and prove the convergence of solutions to the limiting system in the non-equilibrium-diffusion regime. The initial layer for the radiative density is constructed to get the strong convergence in $ L^\infty $ norm. Moreover, we get the exact convergence rates by studying the error system derived from the primitive system, the zeroth-order to the second-order limiting system, and the initial layers.

Keywords:

Mathematics Subject Classification: Primary: 35Q35, 35B25; Secondary: 85A25, 35D35.

Citation:

Full Text(HTML)

Related Papers

Cited by

References

[1]	A. Bensoussan, J.-L. Lions and G. C. Papanicolaou, Boundary layers and homogenization of transport processes, Publ. Res. Inst. Math. Sci., 15 (1979), 53-157. doi: 10.2977/prims/1195188427.
[2]	R. Danchin and B. Ducomet, The low Mach number limit for a barotropic model of radiative flow, SIAM J. Math. Anal., 48 (2016), 1025-1053. doi: 10.1137/15M1009081.
[3]	R. Danchin and B. Ducomet, Diffusive limits for a barotropic model of radiative flow, Confluentes Math., 8 (2016), 31-87. doi: 10.5802/cml.27.
[4]	B. Ducomet, M. Kobera and Š. Nečasová, Global existence of a weak solution for a model in radiation magnetohydrodynamics, Acta Appl. Math., 150 (2017), 43-65. doi: 10.1007/s10440-016-0093-y.
[5]	B. Ducomet and Š. Nečasová, Low Mach number limit for a model of radiative flow, J. Evol. Equ., 14 (2014), 357-385. doi: 10.1007/s00028-014-0217-7.
[6]	B. Ducomet and Š. Nečasová, Diffusion limits in a model of radiation hydrodynamics, Ann. Univ. Ferrara, Sez. 7: Sci. Mat., 61 (2015), 17-59. doi: 10.1007/s11565-014-0214-3.
[7]	B. Ducomet and Š. Nečasová, Singular limits in a model of radiative flow, J. Math. Fluid Mech., 17 (2015), 341-380. doi: 10.1007/s00021-015-0204-y.
[8]	B. Dubroca, M. Seaïd and I. Teleaga, A consistent approach for the coupling of radiation and hydrodynamics at low Mach number, J. Comput. Phys., 225 (2007), 1039-1065. doi: 10.1016/j.jcp.2007.01.011.
[9]	Y. Guo and L. Wu, Geometric correction in diffusive limit of neutron transport equation in 2D convex domains, Arch. Ration. Mech. Anal., 226 (2017), 321-403. doi: 10.1007/s00205-017-1135-y.
[10]	Y. Guo and L. Wu, Regularity of Milne problem with geometric correction in 3D, Math. Models Methods Appl. Sci., 27 (2017), 453-524. doi: 10.1142/S0218202517500075.
[11]	S. Jiang, Q. Ju and Y. Liao, Nonequilibrium-diffusion limit of the compressible Euler-P1 approximation radiation model at low Mach number, SIAM J. Math. Anal., 53 (2021), 2491-2522. doi: 10.1137/20M1344342.
[12]	S. Jiang, F. Li and F. Xie, Nonrelativistic limit of the compressible Navier-Stokes-Fourier-P1 approximation model arising in radiation hydrodynamics, SIAM J. Math. Anal., 47 (2015), 3726-3746. doi: 10.1137/140987596.
[13]	S. Jin, M. Tang and X. Zhang, A spatial-temporal asymptotic preserving scheme for radiation magnetohydrodynamicsin the equilibrium and non-equilibrium diffusion limit, J. Comput. Phys., 452 (2022), 110895. doi: 10.1016/j.jcp.2021.110895.
[14]	Q. Ju, L. Li and Z. C. Zhang, Non-equilibrium-diffusion limit of the compressible Euler radiation model, preprint, arXiv: 2312.15208.
[15]	T. Kato, The Cauchy problem for quasi-linear symmetric hyperbolic systems, Arch. Ration. Mech. Anal., (58) (1975), 181-205. doi: 10.1007/BF00280740.
[16]	F. Li and S. Zhang, The combined non-equilibrium diffusion and low Mach number limits of a model arising in radiation magnetohydrodynamics, J. Differencial Equations, 353 (2023), 114-146. doi: 10.1016/j.jde.2022.12.044.
[17]	G. C. Pomraning, The Equations of Radiation Hydrodynamics, Pergamon Press, Elmsford, New York, 1973.
[18]	I. Teleaga and M. Seaïd, Simplified radiative models for low-Mach number reactive flows, Appl. Math. Model., 32 (2008), 971-991. doi: 10.1016/j.apm.2007.02.021.
[19]	I. Teleaga, M. Seaïd, I. Gasser, A. Klar and J. Struckmeier, Radiation models for thermal flows at low Mach number, J. Comput. Phys., 215 (2006), 506-525. doi: 10.1016/j.jcp.2005.11.015.
[20]	L. Wu, Diffusive limit with geometric correction of unsteady neutron transport equation, Kinet. Relat. Models, 10 (2017), 1163-1203. doi: 10.3934/krm.2017045.
[21]	L. Wu, Diffusive limit of transport equation in 3D convex domains, Peking Math. J., 4 (2021), 203-284. doi: 10.1007/s42543-020-00032-4.
[22]	L. Wu and Y. Guo, Geometric correction for diffusive expansion of steady neutron transport equation, Comm. Math. Phys., 336 (2015), 1473-1553. doi: 10.1007/s00220-015-2315-y.
[23]	F. Xie and C. Klingenberg, A limit problem for three-dimensional ideal compressible radiation magneto-hydrodynamics, Anal. Appl., 16 (2018), 85-102. doi: 10.1142/S0219530516500238.
[24]	X. Zhong and S. Jiang, Local existence and finite-time blow-up in multi-dimensional radiation hydrodynamics, J. Math. Fluid Mech., 9 (2007), 542-564. doi: 10.1007/s00021-005-0213-3.