Publication Cover
Applicable Analysis
An International Journal
Volume 103, 2024 - Issue 3
106
Views
0
CrossRef citations to date
0
Altmetric
Research Article

Weak solutions to the full MHD system with non-homogeneous boundary conditions

ORCID Icon & ORCID Icon
Pages 618-635 | Received 03 Apr 2022, Accepted 31 Mar 2023, Published online: 17 Apr 2023

References

  • Leray J. Sur le mouvement d'un liquide visqueux emplissant l'espace. Acta Math. 1934;63:193–248.
  • Feireisl E, Novotny A. Singular limits in thermodynamics of viscous fluids. 2nd ed., Cham: Birkhäuser/Springer; 2017. (Advances in Mathematical Fluid Mechanics).xlii+524 pp.
  • Chen G, Wang D. Global solutions of nonlinear magnetohydrodynamics with large initial data. J Differ Equ. 2002;182(2):344–376.
  • Ducomet B, Feireisl E. The equations of magnetohydrodynamics: on the interaction between matter and radiation in the evolution of gaseous stars. Commun Math Phys. 2006;266(3):595–629.
  • Fan J, Jiang S, Nakamura G. Vanishing shear viscosity limit in the magnetohydrodynamic equations. Commun Math Phys. 2007;270(3):691–708.
  • Freistühler H, Szmolyan P. Existence and bifurcation of viscous profiles for all intermediate magnetohydrodynamic shock waves. SIAM J Math Anal. 1995;26(1):112–128.
  • Landau L, Bell J, Kearsley M, et al. Electrodynamics of continuous media. Oxford: Pergamon Press; 1960.
  • Jarrín O. Weak-strong uniqueness in weighted L2 spaces and weak suitable solutions in local Morrey spaces for the MHD equations. J Differ Equ. 2021;271:864–915.
  • Liu Y, Zhang T. On weak (measure-valued)-strong uniqueness for compressible MHD system with non-monotone pressure law. Discrete Contin Dyn Syst Ser B. 2022;27(10):6063–6081.
  • Chaudhuri N, Feireisl E. Navier–Stokes–Fourier system with Dirichlet boundary conditions. Appl Anal. 2021;101:4076–4094.
  • Feireisl E, Novotný A. Navier–Stokes–Fourier system with general boundary conditions. Commun Math Phys. 2021;386(2):975–1010.
  • Feireisl E, Jin B, Novotný A. Relative entropies, suitable weak solutions, and weak–strong uniqueness for the compressible Navier–Stokes system. J Math Fluid Mech. 2012;14(4):717–730.
  • Feireisl E, Novotný A. Weak–strong uniqueness property for the full Navier–Stokes–Fourier system. Arch Ration Mech Anal. 2012;204(2):683–706.
  • Feireisl E. Relative entropies in thermodynamics of complete fluid systems. Discrete Contin Dyn Syst. 2012;32(9):3059.3080
  • Lions PL. Mathematical topics in fluid mechanics: vol. 1: incompressible models. New York: Oxford Science Publications. The Clarendon Press, Oxford University Press; 1996. (Oxford Lecture Series in Mathematics and its Applications; Vol. 3).

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.