2014/02/26 by Thierry Gallay, Siniša Slijepčević, Sinisa Slijepcevic · 1 citation
Engineering · Mathematics · #Bounded function #Compressibility #Cylinder #Fluid Dynamics and Turbulent Flows #Fluid dynamics and aerodynamics studies #Incompressible flow #Laminar flow #Navier-Stokes equation solutions #Reynolds number #Uniform boundedness #Vorticity #Zero (linguistics) #math.AP #msc:35B35 #msc:35B40 #msc:35Q30 #msc:76D05
paper · pdf · doi:10.1007/s00021-014-0188-z
24 pages, no figure
arxiv created 2014/02/26 · openalex publication_date 2014/09/16 · arxiv updated 2015/06/18 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We study the incompressible Navier-Stokes equations in the two-dimensional strip ℝ × [0,L], with periodic boundary conditions and no exterior forcing. If the initial velocity is bounded, we prove that the solution remains uniformly bounded for all times, and that the vorticity distribution converges to zero as t → ∞. We deduce that, after a transient period, a laminar regime emerges in which the solution rapidly converges to a shear flow governed by the one-dimensional heat equation. Our approach is constructive and gives explicit estimates on the size of the solution and the lifetime of the turbulent period in terms of the initial Reynolds number.