On Spatial Decay Estimates for Derivatives of Vorticities with Application to Large Time Behavior of the Two-Dimensional Navier–Stokes Flow

2006 ◽  
Vol 10 (1) ◽  
pp. 89-105 ◽  
Author(s):  
Yasunori Maekawa
Keyword(s):  
Stokes Flow ◽  
Large Time ◽  
Large Time Behavior ◽  
Navier Stokes ◽  
Time Behavior ◽  
Decay Estimates ◽  
Two Dimensional ◽  
Spatial Decay ◽  
Derivatives Of

scholarly journals Large Time Behavior for Weak Solutions of the 3D Globally Modified Navier-Stokes Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Junbai Ren
Keyword(s):  
Weak Solutions ◽  
Large Time ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Large Time Behavior ◽  
Navier Stokes ◽  
Heat Semigroup ◽  
Time Behavior ◽  
Decay Estimates ◽  
Navier Stokes Equations

This paper is concerned with the large time behavior of the weak solutions for three-dimensional globally modified Navier-Stokes equations. With the aid of energy methods and auxiliary decay estimates together withLp-Lqestimates of heat semigroup, we derive the optimal upper and lower decay estimates of the weak solutions for the globally modified Navier-Stokes equations asC1(1+t)-3/4≤uL2≤C2(1+t)-3/4,  t>1.The decay rate is optimal since it coincides with that of heat equation.

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