4.5 Article

A Blow-Up Criterion for 3D Nonhomogeneous Incompressible Magnetohydrodynamic Equations with Vacuum

Journal

JOURNAL OF FUNCTION SPACES
Volume 2022, Issue -, Pages -

Publisher

HINDAWI LTD
DOI: 10.1155/2022/7474964

Keywords

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Funding

  1. National Natural Science Foundation of China [61773018, 11971446, 11701525, 12101569]
  2. Natural Science Foundation of Henan [212300410301]
  3. China Scholarship Council [201709440003]

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A blow-up criterion for the strong solutions of the nonhomogeneous incompressible MHD system with vacuum is established, showing the dominant role of the velocity field in the system.
For the strong solutions of the nonhomogeneous incompressible magnetohydrodynamics (MHD) system with vacuum, we establish a blow-up criterion for this system in terms of parallel to u parallel to(C(0,T];L3 (R3))). Moreover, the result generalizes previous ones in Giga (1986) and He and Xin (2005) where homogeneous incompressible Navier-Stokes equations and homogeneous incompressible MHD system are considered, respectively, and demonstrates that the velocity field plays a more dominant role in the MHD system.

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