Uniform regularity of the compressible full Navier–Stokes–Maxwell system

Abstract

In this paper, we prove the uniform regularity of the compressible full Navier–Stokes–Maxwell system in \(\mathbb {T}^3\).

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References

  1. 1.

    Alazard, T.: Low Mach number limit of the full Navier–Stokes equations. Arch. Ration. Mech. Anal. 180, 1–73 (2006)

    MathSciNet  Article  Google Scholar 

  2. 2.

    Dou, C., Jiang, S., Ou, Y.: Low Mach number limit of full Navier–Stokes equations in a 3D bounded domain. J. Differ. Equ. 258, 379–398 (2015)

    MathSciNet  Article  Google Scholar 

  3. 3.

    Fan, J., Jia, Y.: Local well-posedness of the full compressible Navier–Stokes–Maxwell system with vacuum. Kinet. Relat. Models 11(1), 97–106 (2018)

    MathSciNet  Article  Google Scholar 

  4. 4.

    Fan, J., Li, F., Nakamura, G.: A regularity criterion for the 3D full compressible Navier–Stokes–Maxwell system in a bounded domain. Acta Appl. Math. 149, 1–10 (2017)

    MathSciNet  Article  Google Scholar 

  5. 5.

    Fan, J., Li, F., Nakamura, G.: Convergence of the full compressible Navier–Stokes–Maxwell system to the incompressible magnetohydrodynamic equations in a bounded domain. Kinet. Relat. Models 9(3), 443–453 (2016)

    MathSciNet  Article  Google Scholar 

  6. 6.

    Fan, J., Li, F., Nakamura, G.: Convergence of the full compressible Navier-Stokes-Maxwell system to the incompressible magnetohydrodynamic equations in a bounded domain II: global existence case. J. Math. Fluid Mech. 20(2), 359–378 (2018)

    MathSciNet  Article  Google Scholar 

  7. 7.

    Feng, Y., Peng, Y.-J., Wang, S.: Asymptotic behavior of global smooth solutions for full compressible Navier–Stokes–Maxwell equations. Nonlinear Anal. Real World Appl. 19, 105–116 (2014)

    MathSciNet  Article  Google Scholar 

  8. 8.

    Hou, X., Zhu, L.: Serrin-type blowup criterion for full compressible Navier–Stokes–Maxwell system with vacuum. Commun. Pure Appl. Anal. 15(1), 161–183 (2016)

    MathSciNet  Article  Google Scholar 

  9. 9.

    Jiang, S., Li, F.: Convergence of the complete electromagnetic fluid system to the full compressible magnetohydrodynamic equations. Asymptot. Anal. 95(1–2), 161–185 (2015)

    MathSciNet  Article  Google Scholar 

  10. 10.

    Jiang, S., Li, F.: Zero dielectric constant limit to the non-isentropic compressible Euler–Maxwell system. Sci. China Math. 58(1), 61–76 (2015)

    MathSciNet  Article  Google Scholar 

  11. 11.

    Kato, T., Ponce, G.: Commutator estimates and the Euler and Navier–Stokes equations. Commun. Pure Appl. Math. 41, 891–907 (1988)

    MathSciNet  Article  Google Scholar 

  12. 12.

    Kawashima, S.: Smooth global solutions for two-dimensional equations of electro–magneto–fluid dynamics. Jpn. J. Appl. Math. 1, 207–222 (1984)

    Article  Google Scholar 

  13. 13.

    Kawashima, S., Shizuta, Y.: Magnetohydrodynamic approximation of the complete equations for an electromagnetic fluid. Tsukuba J. Math. 10(1), 131–149 (1986)

    MathSciNet  Article  Google Scholar 

  14. 14.

    Kawashima, S., Shizuta, Y.: Magnetohydrodynamic approximation of the complete equations for an electromagnetic fluid II. Proc. Jpn. Acad. 62, 181–184 (1986)

    MathSciNet  Article  Google Scholar 

  15. 15.

    Li, F., Mu, Y.: Low Mach number limit of the full compressible Navier–Stokes–Maxwell system. J. Math. Anal. Appl. 412(1), 334–344 (2014)

    MathSciNet  Article  Google Scholar 

  16. 16.

    Liu, Q., Su, Y.: Large time behavior for the non-isentropic Navier–Stokes–Maxwell system. Math. Methods Appl. Sci. 40(3), 663–679 (2017)

    MathSciNet  Article  Google Scholar 

  17. 17.

    Metivier, G., Schochet, S.: The incompressible limit of the non-isentropic Euler equations. Arch. Ration. Mech. Anal. 158, 61–90 (2001)

    MathSciNet  Article  Google Scholar 

  18. 18.

    Mi, Y., Gao, J.: Long-time behavior of solution for the compressible Navier–Stokes–Maxwell equations in \(R^3\). Math. Methods Appl. Sci. 41(4), 1424–1438 (2018)

    MathSciNet  Article  Google Scholar 

  19. 19.

    Tan, Z., Tong, L.: Asymptotic behavior of the compressible non-isentropic Navier–Stokes–Maxwell system in \(R^3\). Kinet. Relat. Models 11(1), 191–213 (2018)

    MathSciNet  Article  Google Scholar 

  20. 20.

    Triebel, H.: Theory of function spaces. In: Monographs in mathematics. Birkhäuser, Boston (1983)

  21. 21.

    Vol’pert, A.I., Hudjaev, S.I.: The Cauchy problem for composite systems of nonlinear differential equations. Math. USSR. SB 16, 504–528 (1972)

    MathSciNet  Google Scholar 

  22. 22.

    Wang, W., Xu, X.: Large time behavior of solution for the full compressible Navier–Stokes–Maxwell system. Commun. Pure Appl. Anal. 14(6), 2283–2313 (2015)

    MathSciNet  Article  Google Scholar 

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Acknowledgements

The authors are indebted to the referees for the nice comments. Fan was supported by NSFC (Grant No. 11971234). Li was supported in part by NSFC (Grant Nos. 11271184, 11671193) and A Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions.

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Correspondence to Fucai Li.

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Fan, J., Li, F. & Nakamura, G. Uniform regularity of the compressible full Navier–Stokes–Maxwell system. Z. Angew. Math. Phys. 72, 3 (2021). https://doi.org/10.1007/s00033-020-01429-y

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Keywords

  • Compressible full Navier–Stokes-Maxwell system
  • Uniform regularity
  • Non-isentropic Euler–Maxwell system

Mathematics Subject Classification

  • 76W05
  • 35Q60
  • 35B25