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A class of exact solutions for N-dimensional incompressible magnetohydrodynamic equations

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Abstract

In this paper, a sufficient and necessary condition is presented for existence of a class of exact solutions to N-dimensional incompressible magnetohydrodynamic (MHD) equations. Such solutions can be explicitly expressed by appropriate formulae. Once the required matrices are chosen, solutions to the MHD equations are directly constructed.

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References

  1. Duvaut, G. and Lions, J. L. Inéquations en thermoélasticitéet magnétohydrodynamique. Archive for Rational Mechanics Analysis, 46, 241–279 (1972)

    Article  MathSciNet  MATH  Google Scholar 

  2. Tran, C. V., Yu, X., and Zhai, Z. On global regularity of 2D generalized magnetohydrodynamicsequations. Journal of Differential Equations, 254, 4194–4216 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  3. Wu, J. Bounds and new approaches for the 3D MHD equations. Journal of Nonlinear Science, 12, 395–413 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  4. Kato, T. Remanks on the Euler and Navier-Stokes equations in R2, part 2. Proccedings of Symposium in Pure Mathematics, 45, 1–7 (1986)

    Google Scholar 

  5. Hui, W. H. Exact solutions of the unsteady two-dimensional Navier-Stokes equations. Journal of Applied Mathematical Physics, 38, 689–702 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  6. Zelik, S. Spatially nondecaying solutions of 2D Navier-Stokes equations in a strip. Glasgow Mathematical Journal, 49, 525–588 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  7. Zelik, S. Weak spatially non-decaying solutions for the 3D Navier-Stokes equations in cylindrical domains. Instability in Models Connected with Fluid Flows, 7, 255–327 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  8. Arnold, V. I. Sur la topologie des ecoulements stationnaires des fluides parfaits. Comptes Rendus Hebdomadaires Des séances De L’académie Des Sciences, 261, 17–20 (1965)

    MATH  Google Scholar 

  9. Bacciotti, F. and Chiuderi, C. Axisymmetric magnetohydrodynamic equations: exact solutions for stationary incompressible flows. Physical Fluids B, 4, 35–43 (1992)

    Article  MathSciNet  Google Scholar 

  10. Fan, J. H. and Ozawa, T. Regularity criteria for the 2D MHD system with horizontal dissipation and horizontal magnetic diffusion. Kinetic and Related Models, 7, 45–56 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  11. Ye, Z. Two regularity criteria to the 2D generalized MHD equations with zero magnetic diffusivity. Journal of Mathematical Analysis and Applications, 420, 954–971 (2014)

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. School of Management, Tianjin Normal University, Tianjin, 300387, China

    Ping Liu

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  1. Ping Liu
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Correspondence to Ping Liu.

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Liu, P. A class of exact solutions for N-dimensional incompressible magnetohydrodynamic equations. Appl. Math. Mech.-Engl. Ed. 37, 209–214 (2016). https://doi.org/10.1007/s10483-016-2025-8

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  • DOI: https://doi.org/10.1007/s10483-016-2025-8

Keywords

Chinese Library Classification

2010 Mathematics Subject Classification

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