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The 3D incompressible Hall magneto-hydrodynamics equations with partial hyperdissipation

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  • Yuan, Baoquan
  • Li, Chaoying

Abstract

Similarly as the 3D Navier–Stokes equation, the regularity and uniqueness of weak solutions for the 3D standard Hall-MHD equations remain completely open. Wan obtained the global smooth solutions for the incompressible Hall-MHD equations with hyperdissipation (−Δ)α and (−Δ)β when α≥54,β≥74 in (Global regularity for generalized Hall-magnetohydrodynamics systems, Wan (2015) [21]). We obtained the global regularity for the Hall-MHD equations with a logarithmic reduction in the dissipation in (Global regularity for a class of generalized Hall-magnetohydrodynamics equations, Yuan and Li (2018)). In this paper, we prove the global existence and uniqueness in the H1-functional setting by energy method for the three-dimensional incompressible Hall-MHD equations with fractional partial dissipation, which improve Wan’s result by making a different type of reduction in the dissipation.

Suggested Citation

  • Yuan, Baoquan & Li, Chaoying, 2019. "The 3D incompressible Hall magneto-hydrodynamics equations with partial hyperdissipation," Applied Mathematics and Computation, Elsevier, vol. 359(C), pages 308-332.
    • Handle: RePEc:eee:apmaco:v:359:y:2019:i:c:p:308-332
    DOI: 10.1016/j.amc.2019.04.055
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    1. Ye, Zhuan & Zhang, Zujin, 2017. "A remark on regularity criterion for the 3D Hall-MHD equations based on the vorticity," Applied Mathematics and Computation, Elsevier, vol. 301(C), pages 70-77.
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