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On the behavior of the solutions of the Navier-Stokes equations at vanishing viscosity

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On the behavior of the solutions of the Navier-Stokes equations at vanishing viscosity ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA Classe di Scienze ROGER TEMAM XIAOMINGWANG On the behavior of the solutions of the Navier-Stokes equations at vanishing viscosity Annali della Scuola Normale Superiore di Pisa, Classe di Scienze 4e série, tome 25, no 3-4 (1997), p. 807-828. <http://www.numdam.org/item?id=ASNSP_1997_4_25_3-4_807_0> © Scuola Normale Superiore, Pisa, 1997, tous droits réservés. L’accès aux archives de la revue « Annali della Scuola Normale Superiore di Pisa, Classe di Scienze » (http://www.sns.it/it/edizioni/riviste/annaliscienze/) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisa- tion commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/ 807 On the Behavior of the Solutions of the Navier-Stokes Equations at Vanishing Viscosity ROGER TEMAM - XIAOMING WANG Dedicated to the Memory of Ennio De Giorgi Abstract. In this article we establish partial results concerning the convergence of the solutions of the Navier-Stokes equations to that of the Euler equations. Namely, we prove convergence on any finite interval of time, in space dimension two, under a physically reasonable assumption. We consider the flow in a channel or the flow in a general bounded domain. 1. - Introduction The large Reynolds number (or small viscosity) behavior of wall bounded flows is an outstanding problem in mathematics and physics. Many articles are devoted to this problem in the fluid mechanic and mathematical literatures. This includes the well-known works of W. Eckhaus [E], P. Fife [F], T. Kato [Kl], J. L. Lions [Lo2], O. Oleinik [0] and M. I. Vishik and L. A. Lyustemik [VL] among the mat

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