In a recent paper, Vishik proved the global well-posedness of the two-dimensional Euler equation in the critical Besov space B2,1 2. In the present paper we prove that Navier-Stokes system is globally well-posed in B2,1 2, with uniform estimates on the viscosity. We prove also a global result of inviscid limit. The convergence rate in L2 is of order ν.
ASJC Scopus subject areas