Upper bounds for the attractor dimension of damped Navier-Stokes equations in $\mathbb R^2$

<abstract><p>We construct generalized solutions for the Keller-Segel system with a degradation source coupled to Navier Stokes equations in three dimensions, in case that the power of degradation is smaller than quadratic. Furthermore, if the logistic type source is purely damping with no growing effect, we prove that solutions converge to zero in some norms and provide upper bounds of convergence rates in time.</p></abstract>

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Attractor dimension and small length scale estimates for the three-dimensional Navier - Stokes equations

Nonlinearity ◽

10.1088/0951-7715/10/1/007 ◽

1997 ◽

Vol 10 (1) ◽

pp. 109-119 ◽

Cited By ~ 16

Author(s):

J D Gibbon ◽

E S Titi

Keyword(s):

Stokes Equations ◽

Three Dimensional ◽

Navier Stokes ◽

Length Scale ◽

Small Length ◽

Attractor Dimension ◽

Navier Stokes Equations ◽

Small Length Scale

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Remarks on the asymptotic behaviour of solutions to the compressible Navier–Stokes equations in the half-line

Proceedings of the Royal Society of Edinburgh Section A Mathematics ◽

10.1017/s030821050200032x ◽

2002 ◽

Vol 132 (03) ◽

pp. 627

Keyword(s):

Asymptotic Behaviour ◽

Stokes Equations ◽

Half Line ◽

Navier Stokes ◽

Navier Stokes Equations ◽

Asymptotic Behaviour Of Solutions

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Effects of stator splitter blades on aerodynamic performance of a single-stage transonic axial compressor

JOURNAL OF MECHANICAL ENGINEERING AND SCIENCES ◽

10.15282/jmes.14.4.2020.05.0579 ◽

2020 ◽

Vol 14 (4) ◽

pp. 7369-7378

Author(s):

Ky-Quang Pham ◽

Xuan-Truong Le ◽

Cong-Truong Dinh

Keyword(s):

Stokes Equations ◽

Three Dimensional ◽

Axial Compressor ◽

Aerodynamic Performance ◽

Numerical Results ◽

Single Stage ◽

Navier Stokes ◽

Navier Stokes Equations ◽

Operating Stability ◽

Length Coverage

Splitter blades located between stator blades in a single-stage axial compressor were proposed and investigated in this work to find their effects on aerodynamic performance and operating stability. Aerodynamic performance of the compressor was evaluated using three-dimensional Reynolds-averaged Navier-Stokes equations using the k-e turbulence model with a scalable wall function. The numerical results for the typical performance parameters without stator splitter blades were validated in comparison with experimental data. The numerical results of a parametric study using four geometric parameters (chord length, coverage angle, height and position) of the stator splitter blades showed that the operational stability of the single-stage axial compressor enhances remarkably using the stator splitter blades. The splitters were effective in suppressing flow separation in the stator domain of the compressor at near-stall condition which affects considerably the aerodynamic performance of the compressor.

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