Partial Differential Equations/Mathematical Problems in Mechanics
On the convergence at infinity of the Leray solution of the two-dimensional Navier–Stokes equations to the prescribed asymptotic value
Comptes Rendus. Mathématique, Volume 336 (2003) no. 9, pp. 739-744.

In this Note we prove that v L , the Leray velocity solution to the steady incompressible, two-dimensional Navier–Stokes equations, tends at infinity to the prescribed vector v . We show also that the sequence (v R i ,p R i ) of Leray solutions to the same boundary value problem in the bounded domains Ω R i ,i, converges quasi-uniformly in Ω ¯ to (v L ,p L ).

Dans cette Note on prouve que v L , la solution vitesse de Leray des équations stationnaires, incompressibles, bidimensionnelles de Navier–Stokes, tend à l'infini vers le vecteur imposé v . On montre aussi que la suite (v R i ,p R i ) de solutions de Leray du même problème aux limites dans les domaines bornés Ω R i ,i, converge quasi-uniformément dans Ω ¯ vers (v L ,p L ).

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Accepted:
Published online:
DOI: 10.1016/S1631-073X(03)00127-4
Socolescu, Dan 1

1 Fachbereich Mathematik, Universität Kaiserslautern, Erwin-Schrödinger-Strasse, 67663 Kaiserslautern, Germany
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Socolescu, Dan. On the convergence at infinity of the Leray solution of the two-dimensional Navier–Stokes equations to the prescribed asymptotic value. Comptes Rendus. Mathématique, Volume 336 (2003) no. 9, pp. 739-744. doi : 10.1016/S1631-073X(03)00127-4. http://www.numdam.org/articles/10.1016/S1631-073X(03)00127-4/

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