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;.

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;.

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.

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.

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.

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