On the regularity criteria for weak solutions to the magnetohydrodynamic equations

By Cheng He, Yun Wang. 2007

140 citations recorded by the source corpus.

Abstract We study the regularity criteria for weak solutions to the incompressible magnetohydrodynamic equations. Some regularity criteria are obtained for weak solutions to the magnetohydrodynamic equations, which generalize the results in [C. He, Z. Xin, On the regularity of solutions to the magneto-hydrodynamic equations, J. Differential Equations 213 (2) (2005) 235–254]. Our results reveal that the velocity field of the fluid plays a more dominant role than the magnetic field does on the regularity of solutions to the magnetohydrodynamic equations.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/16455a2c7ccfe4881a256ed68307fd4242fcd2bd

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In Applied Mathematics

In Mathematical Physics

Citations in the corpus

Regularity criteria for the solutions to the 3D MHD equations in the multiplier space (2010, background): “Part of them are listed here: Chen et al. [1] proved regularity by adding condition on ∆j( ∇× u); He and Wang [ 3 ] extended it to the weak-L p space L p,∞ ;W ang [9] proved regularity for u ∈ L 2 (0 ,T , BM O); Wu [10] considered the velocity field being in the homogeneous Besov space; regularity w”
On regularity criteria for weak solutions to the micropolar fluid equations in Lorentz space (2010, methodology): “Later, Zhou [36] improved these regularity criteria imposed only on u or its gradient ∇ u , and He and Wang [11] improved them to weak L p spaces, imposed only on u or its gradient ∇ u ; Chen, Miao and Zhang [6] also improved the criteria to a more general Besov-type space on Littlewood-Paley…”