Stabilization of the chemotaxis–Navier–Stokes equations: maximal regularity approach

2021 ◽  
pp. 125422
Author(s):  
Keiichi Watanabe
Keyword(s):  
Maximal Regularity ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations

scholarly journals On the Navier–Stokes equations on surfaces

2020 ◽  
Author(s):  
Jan Prüss ◽  
Gieri Simonett ◽  
Mathias Wilke
Keyword(s):  
Viscous Fluid ◽  
Vector Fields ◽  
Maximal Regularity ◽  
Stokes Equations ◽  
Killing Vector ◽  
Navier Stokes ◽  
Well Posedness ◽  
Exponential Rate ◽  
Killing Vector Fields ◽  
Navier Stokes Equations

Abstract We consider the motion of an incompressible viscous fluid that completely covers a smooth, compact and embedded hypersurface $$\Sigma $$ Σ without boundary and flows along $$\Sigma $$ Σ . Local-in-time well-posedness is established in the framework of $$L_p$$ L p -$$L_q$$ L q -maximal regularity. We characterize the set of equilibria as the set of all Killing vector fields on $$\Sigma $$ Σ , and we show that each equilibrium on $$\Sigma $$ Σ is stable. Moreover, it is shown that any solution starting close to an equilibrium exists globally and converges at an exponential rate to a (possibly different) equilibrium as time tends to infinity.

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

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.

Sensitivity analysis for Navier-Stokes equations on unstructured meshes using complex variables

AIAA Journal ◽  
2001 ◽  
Vol 39 ◽  
pp. 56-63
Author(s):  
W. Kyle Anderson ◽  
James C. Newman ◽  
David L. Whitfield ◽  
Eric J. Nielsen
Keyword(s):  
Sensitivity Analysis ◽  
Stokes Equations ◽  
Unstructured Meshes ◽  
Complex Variables ◽  
Navier Stokes ◽  
Navier Stokes Equations
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