Skip to main content
SpringerLink
Log in

Global Strong Solutions of the 2D Density-Dependent Incompressible Magnetic Bénard Problem

  • Published:
Bulletin of the Malaysian Mathematical Sciences Society Aims and scope Submit manuscript

Abstract

In this paper, we prove global existence of strong solutions to the 2D density-dependent incompressible magnetic Bénard problem in a bounded domain.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Galdi, G.P., Padula, M.: A new approach to energy theory in the stability of fluid motion. Arch. Ration. Mech. Anal. 110, 187–286 (1990)

    Article  MathSciNet  Google Scholar 

  2. Wu, H.: Strong solution to the incompressible MHD equations with vacuum. Comput. Math. Appl. 61, 2742–2753 (2011)

    Article  MathSciNet  Google Scholar 

  3. Huang, X., Wang, Y.: Global strong solution to the 2D nonhomogeneous incompressible MHD system. J. Differ. Equ. 254(2), 511–527 (2013)

    Article  MathSciNet  Google Scholar 

  4. Fan, J., Li, F., Nakamura, G.: Global strong solution to the 2D density-dependent liquid crystal flows with vacuum. Nonlinear Anal. 97, 185–190 (2014)

    Article  MathSciNet  Google Scholar 

  5. Fan, J., Li, F., Nakamura, G.: Regularity criteria for the incompressible magnetohydrodynamic equations with partial viscosity. Anal. Appl. 14(2), 321–339 (2016)

    Article  MathSciNet  Google Scholar 

  6. Fan, J., Liu, D., Zhou, Y.: Uniform global strong solutions of the 2D magnetic Bénard problem in a bounded domain. Appl. Math. Lett. 86, 166–172 (2018)

    Article  MathSciNet  Google Scholar 

  7. Fan, J., Zhou, Y.: Uniform local well-posedness for the density-dependent magnetohydrodynamic equations. Appl. Math. Lett. 24, 1945–1949 (2011)

    Article  MathSciNet  Google Scholar 

  8. Lai, M., Pan, R., Zhao, K.: Initial boundary value problem for two-dimensional viscous Boussinesq equations. Arch. Ration. Mech. Anal. 199, 736–760 (2011)

    Article  MathSciNet  Google Scholar 

  9. Zhao, K.: 2D inviscid heat conductive Boussinesq equations on a bounded domain. Mich. Math. J. 59(2), 329–352 (2010)

    Article  MathSciNet  Google Scholar 

  10. Jin, L., Fan, J., Nakamura, G., Zhou, Y.: Partial vanishing viscosity limit for the 2D Boussinesq system with a slip boundary condition. Bound. Value Probl. 2012, Article ID 20 (2012)

  11. Li, J.: Local existence and uniqueness of strong solutions to the Navier–Stokes equations with nonnegative density. J. Differ. Equ. 263, 6512–6536 (2017)

    Article  MathSciNet  Google Scholar 

  12. Danchin, R., Mucha, P.B.: The incompressible Navier-Stokes equations in vacuum. arXiv: 1705.06061 v2

  13. Mulone, G., Rionero, S.: Necessary and sufficient conditions for nonlinear stability in the magnetic Bénard problem. Arch. Ration. Mech. Anal. 166, 197–281 (2003)

    Article  MathSciNet  Google Scholar 

  14. Cheng, J., Du, L.: On two-dimensional magnetic Bénard problem with mixed partial viscosity. J. Math. Fluid Mech. 17, 769–797 (2015)

    Article  MathSciNet  Google Scholar 

  15. Yamazaki, K.: Global regularity of generalized magnetic Bénard problem. Math. Method Appl. Sci. 40, 2013–2033 (2017)

    MATH  Google Scholar 

  16. Ye, Z.: Global regularity of the 2D magnetic Bénard system with partial dissipation. Adv. Differ. Equ. 23, 193–238 (2018)

    MATH  Google Scholar 

  17. Zhou, Y., Fan, J., Nakamura, G.: Global Cauchy problem for a 2D magnetic Bnard problem with zero thermal conductivity. Appl. Math. Lett. 26(6), 627–630 (2013)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

This work is partially supported by NSFC (11371153 and 11971234), NSF of CQ (cstc2016jcyjA0596), Innovation Team Building at Institutions of Higher Education in Chongqing (CXTDX201601035) and Research project of Chongqing Three Gorges University(17ZP13).

Author information

Authors and Affiliations

  1. Department of Applied Mathematics, Nanjing Forestry University, Nanjing, 210037, People’s Republic of China

    Jishan Fan

  2. College of Mathematics and Statistics, Chongqing Three Gorges University, Chongqing, 404000, People’s Republic of China

    Liangwei Wang

  3. School of Mathematics (Zhuhai), Sun Yat-sen University, Zhuhai, 519082, People’s Republic of China

    Yong Zhou

  4. Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, People’s Republic of China

    Yong Zhou

Authors
  1. Jishan Fan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Liangwei Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yong Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yong Zhou.

Additional information

Communicated by Syakila Ahmad.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Fan, J., Wang, L. & Zhou, Y. Global Strong Solutions of the 2D Density-Dependent Incompressible Magnetic Bénard Problem. Bull. Malays. Math. Sci. Soc. 44, 1749–1769 (2021). https://doi.org/10.1007/s40840-020-01065-9

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40840-020-01065-9

Keywords

Mathematics Subject Classification

Search

Navigation