We study the long-time behavior of infinite-energy solutions to the incompressible Navier-Stokes equations in a two-dimensional exterior domain, with no-slip boundary conditions. The initial data we consider are finite-energy perturbations of a smooth vortex with small circulation at infinity, but are otherwise arbitrarily large. Using a logarithmic energy estimate and some interpolation arguments, we prove that the solution approaches a self-similar Oseen vortex as . This result was obtained in...
We consider the damped wave equation on the whole real line, where is a bistable potential. This equation has travelling front solutions of the form which describe a moving interface between two different steady states of the system, one of which being the global minimum of . We show that, if the initial data are sufficiently close to the profile of a front for large , the solution of the damped wave equation converges uniformly on to a travelling front as . The proof of this global stability...
On sait que toutes les solutions de l’équation de Navier-Stokes dans dont le tourbillon est intégrable convergent lorsque vers un écoulement autosimilaire appelé tourbillon d’Oseen. Dans cet article, nous donnons une estimation du temps nécessaire à la solution pour atteindre un voisinage du tourbillon d’Oseen à partir d’une donnée initiale arbitraire, mais bien localisée en espace. Nous obtenons ainsi une borne supérieure sur le temps de vie de la turbulence bidimensionnelle libre, en fonction...
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