Inviscid limit for the two-dimensional Navier–Stokes system in a critical Besov space

Article type: Research Article

Authors: Hmidi, Taoufik | Keraani, Sahbi

Affiliations: IRMAR, Université de Rennes 1, Campus de Beaulieu, 35 042 Rennes cedex, France E-mails: {thmidi,sahbi.keraani}@univ-rennes1.fr

Abstract: In a recent paper (Arch. Rational Mech. Anal. 145(3) (1998), 197–214), Vishik proved the global well-posedness of the two-dimensional Euler equation in the critical Besov space B2,12. In the present paper we prove that the Navier–Stokes system is globally well-posed in B2,12, with uniform estimates on the viscosity. We prove also a global result of inviscid limit. The convergence rate in L2 is of order ν.

Keywords: Navier–Stokes and Euler equations, inviscid limit, vorticity flows

Journal: Asymptotic Analysis, vol. 53, no. 3, pp. 125-138, 2007