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Currently displaying 1 – 3 of 3

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Global regularity for the 3D MHD system with damping

Zujin Zhang; Xian Yang — 2016

Colloquium Mathematicae

We study the Cauchy problem for the 3D MHD system with damping terms ${ε | u |}^{α - 1} u$ and ${δ | b |}^{β - 1} b$ (ε, δ > 0 and α, β ≥ 1), and show that the strong solution exists globally for any α, β > 3. This improves the previous results significantly.

A regularity criterion for the 3D density-dependent incompressible flow of liquid crystals with vacuum

Zujin Zhang; Xian Yang — 2015

Annales Polonici Mathematici

We consider the Cauchy problem for the 3D density-dependent incompressible flow of liquid crystals with vacuum, and provide a regularity criterion in terms of u and ∇d in the Besov spaces of negative order. This improves a recent result of Fan-Li [Comm. Math. Sci. 12 (2014), 1185-1197].

Remarks on the blow-up criterion for the MHD system involving horizontal components or their horizontal gradients

Zujin Zhang; Xian Yang — 2016

Annales Polonici Mathematici

We study the Cauchy problem for the MHD system, and provide two regularity conditions involving horizontal components (or their gradients) in Besov spaces. This improves previous results.

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