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| We study the incompressible Navier-Stokes equations in the
two-dimensional strip $R \times [0,L]$, 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 $t \to \infty$. 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. |
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