Lower and upper bounds of temporal decay for solutions to n-dimensional hyperviscous Navier–Stokes equations

2021 ◽  
Vol 60 ◽  
pp. 103313
Author(s):  
Lihua Deng ◽  
Haifeng Shang
Keyword(s):  
Stokes Equations ◽  
Upper Bounds ◽  
Navier Stokes ◽  
Lower And Upper Bounds ◽  
Navier Stokes Equations ◽  
Temporal Decay

Temporal and spatial decays for the Navier–Stokes equations

2005 ◽  
Vol 135 (3) ◽  
pp. 461-478 ◽  
Author(s):  
Hyeong-Ohk Bae ◽  
Bum Ja Jin
Keyword(s):  
Decay Rate ◽  
Weak Solutions ◽  
Stokes Equations ◽  
Strong Solutions ◽  
Decay Rates ◽  
Navier Stokes ◽  
Spatial Decay ◽  
Navier Stokes Equations ◽  
Temporal Decay ◽  
Temporal And Spatial

We obtain spatial and temporal decay rates of weak solutions of the Navier–Stokes equations, and for strong solutions. For the spatial decay rate of the weak solutions, the power of the weight given by He and Xin in 2001 does not exceed 3/2;. However, we show the power can be extended up to 5/2;.

On the decay properties of solutions to the non-stationary Navier–Stokes equations in R3

2001 ◽  
Vol 131 (3) ◽  
pp. 597-619 ◽  
Author(s):  
Cheng He ◽  
Zhouping Xin
Keyword(s):  
Stokes Equations ◽  
Strong Solutions ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Temporal Decay ◽  
Decay Properties ◽  
Temporal Variables ◽  
Rates Of Decay ◽  
Stationary Navier Stokes Equations ◽  
Weak And Strong Solutions

In this paper, we study the asymptotic decay properties in both spatial and temporal variables for a class of weak and strong solutions, by constructing the weak and strong solutions in corresponding weighted spaces. It is shown that, for the strong solution, the rate of temporal decay depends on the rate of spatial decay of the initial data. Such rates of decay are optimal.

Temporal and spatial decays for the Navier–Stokes equations

2005 ◽  
Vol 135 (3) ◽  
pp. 461-478 ◽  
Author(s):  
Hyeong-Ohk Bae ◽  
Bum Ja Jin
Keyword(s):  
Decay Rate ◽  
Weak Solutions ◽  
Stokes Equations ◽  
Strong Solutions ◽  
Decay Rates ◽  
Navier Stokes ◽  
Spatial Decay ◽  
Navier Stokes Equations ◽  
Temporal Decay ◽  
Temporal And Spatial

We obtain spatial and temporal decay rates of weak solutions of the Navier–Stokes equations, and for strong solutions. For the spatial decay rate of the weak solutions, the power of the weight given by He and Xin in 2001 does not exceed 3/2;. However, we show the power can be extended up to 5/2;.

On the decay properties of solutions to the non-stationary Navier-Stokes equations in ℝ3

2001 ◽  
Vol 131 (3) ◽  
pp. 597-619
Author(s):  
Cheng He ◽  
Zhouping Xin
Keyword(s):  
Stokes Equations ◽  
Strong Solutions ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Temporal Decay ◽  
Decay Properties ◽  
Temporal Variables ◽  
Rates Of Decay ◽  
Stationary Navier Stokes Equations ◽  
Weak And Strong Solutions

In this paper, we study the asymptotic decay properties in both spatial and temporal variables for a class of weak and strong solutions, by constructing the weak and strong solutions in corresponding weighted spaces. It is shown that, for the strong solution, the rate of temporal decay depends on the rate of spatial decay of the initial data. Such rates of decay are optimal.

scholarly journals Asymptotic Behavior of the Navier-Stokes Equations with Nonzero Far-Field Velocity

2011 ◽  
Vol 2011 ◽  
pp. 1-15 ◽  
Author(s):  
Jaiok Roh
Keyword(s):  
Stokes Equations ◽  
Temporal Stability ◽  
Navier Stokes ◽  
Decay Estimates ◽  
Spatial Decay ◽  
Weighted Function ◽  
Navier Stokes Equations ◽  
Temporal Decay ◽  
Field Velocity ◽  
Temporal Rate

Concerning the nonstationary Navier-Stokes flow with a nonzero constant velocity at infinity, the temporal stability has been studied by Heywood (1970, 1972) and Masuda (1975) inL2space and by Shibata (1999) and Enomoto-Shibata (2005) inLpspaces forp≥3. However, their results did not include enough information to find the spatial decay. So, Bae-Roh (2010) improved Enomoto-Shibata's results in some sense and estimated the spatial decay even though their results are limited. In this paper, we will prove temporal decay with a weighted function by usingLr-Lpdecay estimates obtained by Roh (2011). Bae-Roh (2010) proved the temporal rate becomes slower by(1+σ)/2if a weighted function is|x|σfor0<σ<1/2. In this paper, we prove that the temporal decay becomes slower byσ,where0<σ<3/2if a weighted function is|x|σ. For the proof, we deduce an integral representation of the solution and then establish the temporal decay estimates of weightedLp-norm of solutions. This method was first initiated by He and Xin (2000) and developed by Bae and Jin (2006, 2007, 2008).

scholarly journals Existence of generalized solutions for Keller-Segel-Navier-Stokes equations with degradation in dimension three

2021 ◽  
Vol 4 (5) ◽  
pp. 1-25
Author(s):  
Kyungkeun Kang ◽  
◽  
Dongkwang Kim
Keyword(s):  
Convergence Rates ◽  
Stokes Equations ◽  
Upper Bounds ◽  
Three Dimensions ◽  
Generalized Solutions ◽  
Navier Stokes ◽  
Navier Stokes Equations

<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>

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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