The Reynolds number and large time behaviour for weak solutions of the Navier-Stokes equations

1993 ◽  
Vol 44 (3) ◽  
pp. 587-593
Author(s):  
Hans-Christoph Grunau
Keyword(s):  
Reynolds Number ◽  
Weak Solutions ◽  
Large Time ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Time Behaviour ◽  
Navier Stokes Equations ◽  
Large Time Behaviour

Viscous and inviscid simulations of the start-up vortex

2017 ◽  
Vol 813 ◽  
pp. 53-69
Author(s):  
Paolo Luchini ◽  
Renato Tognaccini
Keyword(s):  
Reynolds Number ◽  
Large Time ◽  
Stokes Equations ◽  
Infinite Plate ◽  
Vortex Method ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Spiral Vortex ◽  
Start Up

Inviscid, unsteady simulations of the roll up of the start-up vortex issuing from a semi-infinite plate are compared with previous simulations of the viscous flow. The inviscid equations were solved by a lumped-vortex method, the two-dimensional, incompressible Navier–Stokes equations in the vorticity–streamfunction formulation modelled the viscous problem. The purpose is to verify whether the irregular behaviour found by the inviscid solution well approximates the unstable evolution of the viscous spiral vortex in the limit of infinitely large time (or equivalently Reynolds number).

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.

Sign in / Sign up

Export Citation Format

Share Document