On energy inequality, smoothness and large time behavior inL 2 for weak solutions of the Navier-Stokes equations in exterior domains

1988 ◽  
Vol 199 (4) ◽  
pp. 455-478 ◽  
Author(s):  
Tetsuro Miyakawa ◽  
Hermann Sohr
Keyword(s):  
Weak Solutions ◽  
Large Time ◽  
Stokes Equations ◽  
Energy Inequality ◽  
Large Time Behavior ◽  
Navier Stokes ◽  
Time Behavior ◽  
Exterior Domains ◽  
Navier Stokes Equations

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.

scholarly journals Decay rate of generalized solutions for equations of a viscous heat-conducting gas

2021 ◽  
Author(s):  
Zhilei Liang
Keyword(s):  
Large Time ◽  
Stokes Equations ◽  
Large Time Behavior ◽  
Ideal Gas ◽  
Generalized Solutions ◽  
Navier Stokes ◽  
Heat Conducting ◽  
Time Behavior ◽  
Navier Stokes Equations ◽  
Viscous Heat

The large time behavior is considered for the solutions of the Navier-Stokes equations for one-dimensional viscous polytropic ideal gas in unbounded domains. Using the local anti-derivatives functions technique, we obtain the power type decay estimates for the generalized solutions as time goes to infinity

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