Limite non visqueuse pour le système de Navier–Stokes dans un espace critique

In a recent paper, Vishik proved the global well-posedness of the two-dimensional Euler equation in the critical Besov space B_2,1². In the present paper we prove that Navier–Stokes system is globally well-posed in B_2,1², with uniform estimates on the viscosity. We prove also a global result of inviscid limit. The convergence rate in L² is of order ν. To cite this article: T. Hmidi, S. Keraani, C. R. Acad. Sci. Paris, Ser. I 338 (2004).