Naslov
Uniform Boundedness and Long-Time Asymptotics for the Two-Dimensional Navier–Stokes Equations in an Infinite Cylinder

Autori
Gallay, Thierry ; Slijepčević, Siniša

Izvornik
Journal of mathematical fluid mechanics (1422-6928) 17 (2015), 1; 23-46

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Navier–Stokes equations; global existence; uniform bounds; long-time behavior

Sažetak
The incompressible Navier–Stokes equations are considered in the two-dimensional strip TeX, with periodic boundary conditions and no exterior forcing. If the initial velocity is bounded, it is shown that the solution remains uniformly bounded for all time, and that the vorticity distribution converges to zero as TeX. This implies, after a transient period, the emergence of a laminar regime in which the solution rapidly converges to a shear flow described by the one-dimensional heat equation in an appropriate Galilean frame. The approach is constructive and provides explicit estimates on the size of the solution and the lifetime of the turbulent period in terms of the initial Reynolds number.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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