Naslov
Energy bounds for the two-dimensional Navier- Stokes equations in an infinite cylinder

Autori
Slijepčević, Siniša ; Gallay, Thierry

Izvornik
Communications in partial differential equations (0360-5302) 39 (2014), 9; 1741-1769

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

Ključne riječi
Navier-Stokes equation; attractors; limit set; uniform convergence; energy estimates

Sažetak
We consider the incompressible Navier-Stokes equation in the cylinder R × T, with no exterior forcing, and we investigate the long- time behavior of solutions arising from merely bounded initial data. Although we do not know if such solutions stay uniformly bounded for all times, we prove that they converge in an appropriate sense to the family of spatially homogeneous equilibria as t goes to infinity. Convergence is uniform on compact subdomains, and holds for all times except on a sparse subset of the positive real axis. We also improve the known upper bound on the L1 norm of the solutions, although our results in this direction are not optimal. Our approach is based on a detailed study of the local energy dissipation in the system, in the spirit of a recent work devoted to a class of dissipative partial differential equations with a formal gradient structure.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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