Global existence of weak and strong solutions to Cucker–Smale–Navier–Stokes equations inR2

2016 ◽  
Vol 27 ◽  
pp. 158-182 ◽  
Author(s):  
Young-Pil Choi ◽  
Jihoon Lee
Keyword(s):  
Global Existence ◽  
Stokes Equations ◽  
Strong Solutions ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Weak And Strong Solutions

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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