scholarly journals Divergence-free Scott--Vogelius Elements on Curved Domains

2021 ◽  
Vol 59 (2) ◽  
pp. 1090-1116
Author(s):  
Michael Neilan ◽  
Baris Otus
Keyword(s):  
Curved Domains ◽  
Divergence Free

Shear-free perfect fluids with divergence free magnetic Weyl curvature

2008 ◽  
Vol 30 ◽  
pp. 241-244
Author(s):  
N. Van den Bergh ◽  
H. Reza Karimian
Keyword(s):  
Weyl Curvature ◽  
Perfect Fluids ◽  
Divergence Free

scholarly journals Symmetry-induced nonlocal divergence-free currents in two-dimensional quantum scattering

2021 ◽  
Vol 103 (3) ◽  
Author(s):  
M. A. Metaxas ◽  
P. Schmelcher ◽  
F. K. Diakonos
Keyword(s):  
Quantum Scattering ◽  
Two Dimensional ◽  
Divergence Free

Solving Magnetohydrodynamic Equations Without Special Treatment for Divergence-Free Magnetic Field

AIAA Journal ◽  
2004 ◽  
Vol 42 (12) ◽  
pp. 2605-2608 ◽  
Author(s):  
Moujin Zhang ◽  
S.-T. John Yu ◽  
Shang-Chuen Lin ◽  
Sin-Chung Chang ◽  
Isaiah Blankson
Keyword(s):  
Magnetic Field ◽  
Special Treatment ◽  
Magnetohydrodynamic Equations ◽  
Divergence Free

Pseudo-Z symmetric space-times with divergence-free Weyl tensor and pp-waves

2016 ◽  
Vol 13 (02) ◽  
pp. 1650015 ◽  
Author(s):  
Carlo Alberto Mantica ◽  
Young Jin Suh
Keyword(s):  
Symmetric Space ◽  
Weyl Tensor ◽  
Killing Vector ◽  
Complete Classification ◽  
Space Time ◽  
Conformal Killing ◽  
Conformally Flat ◽  
Conformal Curvature ◽  
Wave Space ◽  
Divergence Free

In this paper we present some new results about [Formula: see text]-dimensional pseudo-Z symmetric space-times. First we show that if the tensor Z satisfies the Codazzi condition then its rank is one, the space-time is a quasi-Einstein manifold, and the associated 1-form results to be null and recurrent. In the case in which such covector can be rescaled to a covariantly constant we obtain a Brinkmann-wave. Anyway the metric results to be a subclass of the Kundt metric. Next we investigate pseudo-Z symmetric space-times with harmonic conformal curvature tensor: a complete classification of such spaces is obtained. They are necessarily quasi-Einstein and represent a perfect fluid space-time in the case of time-like associated covector; in the case of null associated covector they represent a pure radiation field. Further if the associated covector is locally a gradient we get a Brinkmann-wave space-time for [Formula: see text] and a pp-wave space-time in [Formula: see text]. In all cases an algebraic classification for the Weyl tensor is provided for [Formula: see text] and higher dimensions. Then conformally flat pseudo-Z symmetric space-times are investigated. In the case of null associated covector the space-time reduces to a plane wave and results to be generalized quasi-Einstein. In the case of time-like associated covector we show that under the condition of divergence-free Weyl tensor the space-time admits a proper concircular vector that can be rescaled to a time like vector of concurrent form and is a conformal Killing vector. A recent result then shows that the metric is necessarily a generalized Robertson–Walker space-time. In particular we show that a conformally flat [Formula: see text], [Formula: see text], space-time is conformal to the Robertson–Walker space-time.

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