On existence of global solutions to the two-dimensional Navier-Stokes equations for a compressible viscous fluid

1995 ◽  
Vol 36 (6) ◽  
pp. 1108-1141 ◽  
Author(s):  
V. A. Vaigant ◽  
A. V. Kazhikhov
Keyword(s):  
Viscous Fluid ◽  
Stokes Equations ◽  
Global Solutions ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Compressible Viscous Fluid ◽  
Navier Stokes Equations

On asymptotic stability of global solutions in the weak L2 space for the two-dimensional Navier–Stokes equations

Analysis ◽  
2015 ◽  
Vol 35 (4) ◽  
Author(s):  
Yasunori Maekawa
Keyword(s):  
Asymptotic Stability ◽  
Stokes Equations ◽  
Global Solutions ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations

AbstractIn this paper we prove the asymptotic stability of small global solutions in the weak

scholarly journals Two-dimensional incompressible viscous flow around a thin obstacle tending to a curve

2009 ◽  
Vol 139 (6) ◽  
pp. 1237-1254 ◽  
Author(s):  
Christophe Lacave
Keyword(s):  
Viscous Fluid ◽  
Viscous Flow ◽  
Recent Work ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Incompressible Viscous Flow ◽  
Limit Solution ◽  
Thin Obstacle

Building on a recent work, we consider a two-dimensional viscous fluid in the exterior of a thin obstacle shrinking to a curve, proving convergence to a solution of the Navier–Stokes equations in the exterior of a curve. The uniqueness of the limit solution is also shown.>

Direct simulation of transition in an oscillatory boundary layer

1998 ◽  
Vol 371 ◽  
pp. 207-232 ◽  
Author(s):  
G. VITTORI ◽  
R. VERZICCO
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Turbulent Regime ◽  
Two Dimensional ◽  
Temporal Development ◽  
Direct Simulation ◽  
Navier Stokes Equations ◽  
Oscillatory Boundary Layer

Numerical simulations of Navier–Stokes equations are performed to study the flow originated by an oscillating pressure gradient close to a wall characterized by small imperfections. The scenario of transition from the laminar to the turbulent regime is investigated and the results are interpreted in the light of existing analytical theories. The ‘disturbed-laminar’ and the ‘intermittently turbulent’ regimes detected experimentally are reproduced by the present simulations. Moreover it is found that imperfections of the wall are of fundamental importance in causing the growth of two-dimensional disturbances which in turn trigger turbulence in the Stokes boundary layer. Finally, in the intermittently turbulent regime, a description is given of the temporal development of turbulence characteristics.

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