Global existence of a diffusion limit with damping for the compressible radiative Euler system coupled to an electromagnetic field

Xavier Blanc, Bernard Ducomet, Šárka Nečasová

Abstract


We study the Cauchy problem for a system of equations corresponding to a singular limit of radiative hydrodynamics, namely the 3D radiative compressible Euler system coupled to an electromagnetic field through the MHD approximation. Assuming the presence of damping together with suitable smallness hypotheses for the data, we prove that this problem admits a unique global smooth solution.

Keywords


Compressible; Euler; magnetohydrodynamics; radiation hydrodynamics

Full Text:

PREVIEW FULL TEXT

References


C. Beauchard and E. Zuazua, Large time asymptotics for partially dissipative hyperbolic systems, Arch. Rational Mech. Anal. 199 (2011), 177–227.

S. Benzoni-Gavage and D. Serre, Multi-Dimensional Hyperbolic Partial Differential Equations, Oxford Science Publications, 2007.

X. Blanc and B. Ducomet, Weak and strong solutions of equations of compressible magnetohydrodynamics, Handbook of Mathematical Analysis in Mechanics of Viscous Fluids (Y. Giga and A. Novotny, eds), Springer, Cham, 2016.

X. Blanc, B. Ducomet and Š. Nečasová, On some singular limits in damped radiation hydrodynamics, J. Hyperbolic Differ. Equ. 13 (2016), 249–271.

C. Buet and B. Després, On some singular limits in damped radiation hydrodynamics. Asymptotic analysis of fluid models for the coupling of radiation and hydrodynamics, J. Quant. Spectrosc. Radiat. Transfer 85 (2004) 385–418.

H. Cabannes, Theoretical Magnetohydrodynamics, Academic Press, New York, 1970.

A.R. Choudhuri, The Physics of Fluids and Plasmas: an Introduction for Astrophysicists, Cambridge University Press, 1998.

G.S. Dulikravich and S.R. Lynn, Unified electro-magneto-fluid dynamics: a survey of mathematical models, Int. J. Non-Linear Mechanics 32 (1997), 923–932.

E. Feireisl and A. Novotný, Singular Limits in Thermodynamics of Viscous Fluids, Birkhäuser, Basel, 2009.

B. Hanouzet and R. Natalini, Global existence of smooth solutions for partially dissipative hyperbolic systems with a convex entropy, Arch. Ration. Mech. Anal. 69 (2003), no. 2, 89–117.

I. Imai, General principles of magneto-fluid dynamics., Suppl. Progress Theor. Phys. 24 (1962), 1–34.

R.E. Kalman, P.L. Falb and M. A. Arbib, Topics in Mathematical System Theory McGraw–Hill Book Co., New York–Toronto, Ont.–London, 1969.

C. Lin and T. Goudon, Global existence of the equilibrium diffusion model in radiative hydrodynamics, Chin. Ann. Math. Ser. B 32 (2011), 549–568.

R.B. Lowrie, J.E. Morel and J.A. Hittinger, The coupling of radiation and hydrodynamics, Astrophys. J. 521 (1999) 432–450.

A. Majda, Compressible FluidFflow and Systems of Conservation Laws in Several Variables, Springer–Verlag, New York, Berlin, Heidelberg, Tokyo, 1984.

P.A. Markowich, C. Ringhofer and C. Schmeiser, Semiconductor Equations, Springer–Verlag, New York, Berlin, Heidelberg, Tokyo, 1990.

D. Mihalas and B. Weibel-Mihalas, Foundations ofRradiation Hydrodynamics, Oxford University Press, New York, 1984.

T. Nishida, Nonlinear Hyperbolic Hquations and Related Topics in Fluid Dynamics, Publications Mathématiques d’Orsay, No. 78–02, Département de Mathématique, Université de Paris–Sud, Orsay, 1978.

G.C. Pomraning, Radiation Hydrodynamics, Dover Publications, Inc., Mineola, New York, 2005.

D. Serre, Systèmes de Lois de Conservation I, II, Diderot Editeur, Arts et Sciences, Paris, New York, Amsterdam, 1996.

D. Serre, Systems of Conservation Laws with Dissipation, Lecture Notes SISSA, 2007.

Y. Shizuta and S. Kawashima Systems of equation of hyperbolic–parabolic type with application to the discrete Boltzmann equation, Hokkaido Math. J. 14 (1985), 249–275.

Y. Ueda, S. Wang and S. Kawashima, Dissipative structure of the regularity-loss type and time asynptotic decay of solutions for the Euler–Maxwell system, SIAM J. Math. Anal. 44 (2012), 2002–2017.


Refbacks

  • There are currently no refbacks.

Partnerzy platformy czasopism