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Applicable Analysis
An International Journal
Volume 97, 2018 - Issue 14
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Articles

Global regularity for a special family of axisymmetric solutions to the three-dimensional magnetic Bénard problem

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Pages 2533-2543 | Received 31 May 2017, Accepted 03 Sep 2017, Published online: 18 Sep 2017

References

  • Mulone G, Rionero S. Necessary and sufficient conditions for nonlinear stability in the magnetic Benard problem. Arch Ration Mech Anal. 2003;166:197–218.
  • Nakamura M. On the magnetic Benard problem. J Fac Sci Univ Tokyo Sec IA Math. 1991;38:359–393.
  • Zhou Y, Fan JS, Nakamura G. Global Cauchy problem for a 2D magnetic Bénard problem with zero thermal conductivity. Appl Math Lett. 2013;26:627–630.
  • Cheng JF, Du LL. On two-dimensional magnetic Bénard problem with mixed partial viscosity J Math Fluid Mech. 2015;17:769–797.
  • Lei Z. On axially symmetric incompressible magnetohydrodynamics in three dimensions. J Differ Equ. 2015;259:3202–3215.
  • Miao CX, Zheng XX. On the global well-posedness for the Boussinesq system with horizontal dissipation. Commun Math Phys. 2013;321:33–67.
  • Leonardi S, Málek J, Nečas J, et al . On axially symmetric flows in ℝ3. Z Anal Anwendungen. 1999;18:639–649.
  • Lewis JE. Mixed estimates for singular integrals and an application to initial value problems in parabolic differential equations. In: Singular integrals, Chicago, IL, 1966. Proceedings of Symposia in Pure Mathematics. Providence (RI): American Mathematical Society; 1967. p. 218–231.
  • Wolf VW. The equation u'+A(t)u = fin a Hilbert space and Lp -estimates for parabolic equations. J Lond Math Soc. 1982;25:483–497.
  • Kato T, Ponce G. Commutator estimates and the Euler and Navier-Stokes equations. Commun Pure Appl Math. 1988;41:891–907.

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