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1
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Remarks on regularity criteria for the Navier-Stokes equations with axisymmetric data

100%
Zhang Z.
Annales Polonici Mathematici
|
2016
|
tom 117
|
nr 2
181-196
EN
We consider the axisymmetric Navier-Stokes equations with non-zero swirl component. By invoking the Hardy-Sobolev interpolation inequality, Hardy inequality and the theory of $*A_{β}$ (1 < β < ∞) weights, we establish regularity criteria involving $u^{r}$, $ω^{z}$ or $ω^{θ}$ in some weighted Lebesgue spaces. This improves many previous results.
2
Content available remote

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

63%
Zhang Z., Yang X.
Annales Polonici Mathematici
|
2016
|
tom 116
|
nr 1
87-99
EN
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.
3
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Global regularity for the 3D MHD system with damping

63%
Zhang Z., Yang X.
Colloquium Mathematicum
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2016
|
tom 145
|
nr 1
107-110
EN
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.
4
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A regularity criterion for the 3D density-dependent incompressible flow of liquid crystals with vacuum

63%
Zhang Z., Yang X.
Annales Polonici Mathematici
|
2015
|
tom 115
|
nr 2
165-177
EN
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].
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