Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-22T04:59:55.570Z Has data issue: false hasContentIssue false
  • English
  • Français

A convergence to the Navier–Stokes–Maxwell system with solenoidal Ohm's law from a two-fluid model

Part of: Equations of mathematical physics and other areas of application Partial differential equations

Published online by Cambridge University Press:  26 August 2020

Zeng Zhang
Zeng Zhang*
Affiliation:
School of Science, Wuhan University of Technology, Wuhan, 430070, People's Republic of China ([email protected])
Get access Rights & Permissions [Opens in a new window]

Abstract

We show the incompressible Navier–Stokes–Maxwell system with solenoidal Ohm's law can be derived from the two-fluid incompressible Navier–Stokes–Maxwell system when the momentum transfer coefficient tends to zero. The strategy is based on the decay and dissipative properties of the electromagnetic field.

Keywords

Navier–Stokes equationsMaxwell equationsglobal well-posednessasymptotic process

MSC classification

Primary: 35Q30: Navier-Stokes equations
Secondary: 35Q61: Maxwell equations 35A01: Existence problems
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 151 , Issue 3 , June 2021 , pp. 1094 - 1115
Check for updates
Copyright
Copyright © The Author(s) 2020. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Arsénio, D., Ibrahim, S. and Masmoudi, N.. A derivation of the magnetohydrodynamic system from Navier-Stokes-Maxwell systems. Arch. Ration. Mech. Anal. 216 (2015), 767–812.CrossRefGoogle Scholar
Bahouri, H., Chemin, J.-Y. and Danchin, R.. Fourier analysis and nonlinear partial differential equations (New York: Springer-Verlag, 2011).CrossRefGoogle Scholar
Germain, P., Ibrahim, S. and Masmoudi, N.. Well-posedness of the Navier–Stokes–Maxwell equations. P. R. Soc. Edinburgh 144A (2014), 71–86.CrossRefGoogle Scholar
Ghoul, T., Ibrahim, S. and Shen, S.. Long time behavior of a two-fluid model. Accepted by Adv. Math. Sci. Appl.Google Scholar
Giga, Y., Ibrahim, S., Shen, S. and Yoneda, T.. Global well posedness for a two-fluid model. Differ. Integr. Equ. 31 (2018), 187–214.Google Scholar
Giga, Y. and Yoshida, Z.. On the equations of two-component theory in magnetohydrodynamics. Commun. Part. Differ. Equ. 9 (1984), 503–522.CrossRefGoogle Scholar
Ibrahim, S. and Keraani, S.. Global small solutions for the Navier–Stokes–Maxwell system. SIAM J. Math. Anal. 43 (2011), 2275–2295.CrossRefGoogle Scholar
Jiang, N. and Luo, Y.-L.. Global classical solutions to the two-fluid incompressible Navier–Stokes–Maxwell system with Ohm's law. Commun. Math. Sci. 16 (2018), 561–578.CrossRefGoogle Scholar
Masmoudi, N.. Global well posedness for the Maxwell–Navier–Stokes system in 2D. J. Math. Pures Appl. 93 (2010), 559–571.CrossRefGoogle Scholar