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 Abstract: We consider the convergence in the $L^2$ norm, uniformly in time, of the Navier-Stokes equations with Dirichlet boundary conditions to the Euler equations with slip boundary conditions. We prove that if the Oleinik conditions of no back-flow in the trace of the Euler flow, and of a lower bound for the Navier-Stokes vorticity is assumed in a Kato-like boundary layer, then the inviscid limit holds. Publication Date: Jul-2015 Electronic Publication Date: 4-Mar-2015 Citation: Constantin, Peter, Kukavica, Igor, Vicol, Vlad. (On the inviscid limit of the Navier-Stokes equations, Proc. Amer. Math. Soc. 143 (2015), no. 7, 3075–3090. MR 3336632, https://doi.org/10.1090/S0002-9939-2015-12638-X DOI: 10.1090/S0002-9939-2015-12638-X Pages: 3075-3090 Type of Material: Journal Article Journal/Proceeding Title: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY Version: Author's manuscript