scholarly journals Dynamics for the 3D incompressible Navier-Stokes equations with double time delays and damping

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Wei Shi ◽  
Xiaona Cui ◽  
Xuezhi Li ◽  
Xin-Guang Yang
Keyword(s):  
Time Delays ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Strong Solutions ◽  
Navier Stokes ◽  
Pullback Attractors ◽  
Navier Stokes Equations ◽  
Subcritical Nonlinearity ◽  
Double Time ◽  
Autonomous Dynamical Systems

<p style='text-indent:20px;'>This paper is concerned with the tempered pullback attractors for 3D incompressible Navier-Stokes model with a double time-delays and a damping term. The delays are in the convective term and external force, which originate from the control in engineer and application. Based on the existence of weak and strong solutions for three dimensional hydrodynamical model with subcritical nonlinearity, we proved the existence of minimal family for pullback attractors with respect to tempered universes for the non-autonomous dynamical systems.</p>

scholarly journals Pullback dynamics of a 3D modified Navier-Stokes equations with double delays

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Pan Zhang ◽  
Lan Huang ◽  
Rui Lu ◽  
Xin-Guang Yang
Keyword(s):  
Time Delays ◽  
Energy Equation ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Pullback Attractors ◽  
Navier Stokes Equations ◽  
Convergence Method ◽  
Double Time ◽  
External Forces ◽  
Weak Convergence Method

<p style='text-indent:20px;'>This paper is concerned with the tempered pullback dynamics for a 3D modified Navier-Stokes equations with double time-delays, which includes delays on external force and convective terms respectively. Based on the property of monotone operator and some suitable hypotheses on the external forces, the existence and uniqueness of weak solutions can be shown in an appropriate functional Banach space. By using the energy equation technique and weak convergence method to achieve asymptotic compactness for the process, the existence of minimal family of pullback attractors has also been derived.</p>

Unique Strong Solutions and V -Attractors of a Three Dimensional System of Globally Modified Navier-Stokes Equations

2006 ◽  
Vol 6 (3) ◽  
Author(s):  
Tomás Caraballo ◽  
José Real ◽  
Peter E. Kloeden
Keyword(s):  
Weak Solutions ◽  
Existence And Uniqueness ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Strong Solutions ◽  
Navier Stokes ◽  
Dimensional System ◽  
Navier Stokes Equations ◽  
Three Dimensional System

AbstractWe prove the existence and uniqueness of strong solutions of a three dimensional system of globally modified Navier-Stokes equations. The flattening property is used to establish the existence of global V -attractors and a limiting argument is then used to obtain the existence of bounded entire weak solutions of the three dimensional Navier-Stokes equations with time independent forcing.

scholarly journals THREE-DIMENSIONAL SYSTEM OF GLOBALLY MODIFIED NAVIER–STOKES EQUATIONS WITH DELAY

2010 ◽  
Vol 20 (09) ◽  
pp. 2869-2883 ◽  
Author(s):  
TOMÁS CARABALLO ◽  
JOSÉ REAL ◽  
ANTONIO M. MÁRQUEZ
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Strong Solutions ◽  
Navier Stokes ◽  
Asymptotic Behavior Of Solutions ◽  
Pullback Attractor ◽  
Dimensional System ◽  
Navier Stokes Equations ◽  
Three Dimensional System ◽  
Equations With Delay

We prove the existence and uniqueness of strong solutions of a three-dimensional system of globally modified Navier–Stokes equations with delay in the locally Lipschitz case. The asymptotic behavior of solutions, and the existence of pullback attractor are also analyzed.

BLOW-UP CRITERIA FOR THE NAVIER–STOKES EQUATIONS OF COMPRESSIBLE FLUIDS

2008 ◽  
Vol 05 (01) ◽  
pp. 167-185 ◽  
Author(s):  
JISHAN FAN ◽  
SONG JIANG
Keyword(s):  
Blow Up ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Strong Solutions ◽  
Compressible Fluids ◽  
Navier Stokes ◽  
Positive Density ◽  
Heat Conducting ◽  
Navier Stokes Equations ◽  
Local Strong Solutions

We study the Navier–Stokes equations of three-dimensional compressible isentropic and two-dimensional heat-conducting flows in a domain Ω with nonnegative density, which may vanish in an open subset (vacuum) of Ω, and with positive density, respectively. We prove some blow-up criteria for the local strong solutions.

Addendum to the Paper “Unique Strong Solutions and V -Attractors of a Three Dimensional System of Globally Modified Navier-Stokes Equations″, Advanced Nonlinear Studies 6 (2006), 411-436

2010 ◽  
Vol 10 (1) ◽  
Author(s):  
Tomás Caraballo ◽  
José Real ◽  
Peter E. Kloeden
Keyword(s):  
Existence And Uniqueness ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Strong Solutions ◽  
Navier Stokes ◽  
Dimensional System ◽  
Uniqueness Of Solutions ◽  
Navier Stokes Equations ◽  
Three Dimensional System

AbstractIn this paper we improve Theorem 7 in [1] which deals with the existence and uniqueness of solutions of the three dimensional globally modified Navier-Stokes equations.

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.

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