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

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 B_2,1². In the present paper we prove that the 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.