On uniqueness of stationary solutions to the Navier–Stokes equations in exterior domains

2012 ◽  
Vol 75 (8) ◽  
pp. 3457-3464 ◽  
Author(s):  
Tomoyuki Nakatsuka
Keyword(s):  
Stokes Equations ◽  
Stationary Solutions ◽  
Navier Stokes ◽  
Exterior Domains ◽  
Navier Stokes Equations

scholarly journals Disconnected stationary solutions for 3D Kolmogorov flow problem: preliminary results

2021 ◽  
Vol 2090 (1) ◽  
pp. 012046
Author(s):  
Nikolay M. Evstigneev
Keyword(s):  
Flow Problem ◽  
Stokes Equations ◽  
Continuation Method ◽  
Fourier Method ◽  
Stationary Solutions ◽  
Navier Stokes ◽  
System Of Nonlinear Equations ◽  
Arc Length ◽  
Navier Stokes Equations ◽  
Numerical Bifurcation

Abstract The extension of the classical A.N. Kolmogorov’s flow problem for the stationary 3D Navier-Stokes equations on a stretched torus for velocity vector function is considered. A spectral Fourier method with the Leray projection is used to solve the problem numerically. The resulting system of nonlinear equations is used to perform numerical bifurcation analysis. The problem is analyzed by constructing solution curves in the parameter-phase space using previously developed deflated pseudo arc-length continuation method. Disconnected solutions from the main solution branch are found. These results are preliminary and shall be generalized elsewhere.

scholarly journals On the steady Navier–Stokes equations in 2D exterior domains

2020 ◽  
Vol 269 (3) ◽  
pp. 1796-1828 ◽  
Author(s):  
Mikhail V. Korobkov ◽  
Konstantin Pileckas ◽  
Remigio Russo
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Exterior Domains ◽  
Navier Stokes Equations
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