scholarly journals The inverse of the divergence operator on perforated domains with applications to homogenization problems for the compressible Navier–Stokes system

2017 ◽  
Vol 23 (3) ◽  
pp. 851-868 ◽  
Author(s):  
Lars Diening ◽  
Eduard Feireisl ◽  
Yong Lu
Keyword(s):  
Stokes System ◽  
Navier Stokes ◽  
Perforated Domains ◽  
Divergence Operator ◽  
Homogenization Problems

scholarly journals Some preliminary observations on a defect Navier–Stokes system

2019 ◽  
Vol 347 (10) ◽  
pp. 677-684 ◽  
Author(s):  
Amit Acharya ◽  
Roger Fosdick
Keyword(s):  
Stokes System ◽  
Navier Stokes

scholarly journals Asymptotic analysis of an optimal control problem for a viscous incompressible fluid with Navier slip boundary conditions

2021 ◽  
pp. 1-21
Author(s):  
Claudia Gariboldi ◽  
Takéo Takahashi
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Boundary Conditions ◽  
Control Problem ◽  
Stokes System ◽  
Navier Stokes ◽  
Slip Boundary Conditions ◽  
Navier Slip ◽  
Slip Boundary ◽  
Navier Slip Boundary Conditions

We consider an optimal control problem for the Navier–Stokes system with Navier slip boundary conditions. We denote by α the friction coefficient and we analyze the asymptotic behavior of such a problem as α → ∞. More precisely, we prove that if we take an optimal control for each α, then there exists a sequence of optimal controls converging to an optimal control of the same optimal control problem for the Navier–Stokes system with the Dirichlet boundary condition. We also show the convergence of the corresponding direct and adjoint states.

Homogenization of the time discretized compressible Navier–Stokes system

2012 ◽  
Vol 75 (4) ◽  
pp. 2486-2498 ◽  
Author(s):  
Hongxing Zhao ◽  
Zheng-an Yao
Keyword(s):  
Stokes System ◽  
Navier Stokes

Development of mixing and isotropy in inviscid homogeneous turbulence

1982 ◽  
Vol 120 ◽  
pp. 155-183 ◽  
Author(s):  
Jon Lee
Keyword(s):  
Dynamical Systems ◽  
Lower Order ◽  
Stokes System ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Fourier Space ◽  
Kolmogorov Entropy ◽  
Navier Stokes Equations ◽  
Constant Energy

We have investigated a sequence of dynamical systems corresponding to spherical truncations of the incompressible three-dimensional Navier-Stokes equations in Fourier space. For lower-order truncated systems up to the spherical truncation of wavenumber radius 4, it is concluded that the inviscid Navier-Stokes system will develop mixing (and a fortiori ergodicity) on the constant energy-helicity surface, and also isotropy of the covariance spectral tensor. This conclusion is, however, drawn not directly from the mixing definition but from the observation that one cannot evolve the trajectory numerically much beyond several characteristic corre- lation times of the smallest eddy owing to the accumulation of round-off errors. The limited evolution time is a manifestation of trajectory instability (exponential orbit separation) which underlies not only mixing, but also the stronger dynamical charac- terization of positive Kolmogorov entropy (K-system).

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