Incompressible limit for the full magnetohydrodynamics flows under strong stratification. (English) Zbl 1229.35210

Summary: We consider the magnetohydrodynamics flows giving rise to a variety of mathematical problems in many areas. We study the incompressible limit problems for magnetohydrodynamics flows under strong stratification.


35Q35 PDEs in connection with fluid mechanics
76W05 Magnetohydrodynamics and electrohydrodynamics
78A25 Electromagnetic theory (general)
80A20 Heat and mass transfer, heat flow (MSC2010)
35A15 Variational methods applied to PDEs
Full Text: DOI


[1] Becker, E., Gasdynamik (1966), Teubner-Verlag: Teubner-Verlag Stuttgart · Zbl 0139.20901
[2] Ducomet, B.; Feireisl, E., The equations of magnetohydrodynamics: On the interaction between matter and radiation in the evolution of gaseous stars, Comm. Math. Phys., 266, 595-629 (2006) · Zbl 1113.76098
[3] Feireisl, E., Stability of flows of real monoatomic gases, Comm. Partial Differential Equations, 31, 325-348 (2006) · Zbl 1092.35077
[4] Feireisl, E.; Novotný, A., The low Mach number limit for the full Navier-Stokes-Fourier system, Arch. Ration. Mech. Anal., 186, 77-107 (2007) · Zbl 1147.76049
[5] Feireisl, E.; Novotný, A., Singular limita in the thermodynamics of viscous fluids, Adv. Math. Fluid Mech. (2009)
[6] Feireisl, E.; Novotný, A.; Petzeltová, H., Lyered incompressible fluid flow equations in the limit of low Mach number and strong stratification, Phys. D, 237, 1466-1487 (2008) · Zbl 1143.76562
[7] Hu, Xianpeng; Wang, Dehua, Global solutions to the three-dimensional full compressible magnetohydrodynamic flows, Comm. Math. Phys., 283, 255-284 (2008) · Zbl 1158.35075
[8] Hu, Xianpeng; Wang, Dehua, Low Mach number limit of viscous compressible magnetohydrodynamic flows, SIAM J. Math. Anal., 41, 1272-1294 (2009) · Zbl 1188.35146
[9] Klainerman, S.; Majda, A., Singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids, Comm. Pure Appl. Math., 34, 481-524 (1981) · Zbl 0476.76068
[10] Kwon, Y.-S.; Trivisa, K., On the incompressible limits for the full magnetohydrodynamics flows, J. Differential Equations, 251, 1990-2023 (2011) · Zbl 1242.35051
[11] Lions, P.-L.; Masmoudi, N., Incompressible limit for a viscous compressible fluid, J. Math. Pures Appl. (9), 77, 585-627 (1998) · Zbl 0909.35101
[12] Antonin Novotny, Michael Ruzicka, Gudrun Thater, Rigorous derivation of the anelastic approximation to the Oberbeck-Boussinesq equations, Asymptot. Anal., in press.; Antonin Novotny, Michael Ruzicka, Gudrun Thater, Rigorous derivation of the anelastic approximation to the Oberbeck-Boussinesq equations, Asymptot. Anal., in press. · Zbl 1306.35097
[13] Novotny, Antonin; Ruzicka, Michael; Thater, Gudrun, Singular limit of the equations of magnetohydrodynamics in the presence of strong stratification, Math. Models Methods Appl. Sci., 21, 115-147 (2011) · Zbl 1429.76124
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.