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In their classical work [20], Caflisch and Sammartino established theinviscid limit and boundary layer expansions of vanishing viscosity solutionsto the incompressible Navier-Stokes equations for analytic data on ahalf-space. It was then subsequently announced in their Comptes rendus article[4] that the results can be extended to include analytic data on an exteriorcircular domain, however the proof appears missing in the literature. Theextension to an exterior domain faces a fundamental difficulty that thecorresponding linear semigroup may not be contractive in analytic spaces as wasthe case on the half-space [19]. In this paper, we resolve this open problemfor a much larger class of initial data. The resolution is due to the fact thatit suffices to propagate solutions that are analytic only near the boundary,following the framework developed in the recent works that involve the boundaryvorticity formulation, the analyticity estimates on the Green function, theadapted geodesic coordinates near a boundary, and the Sobolev-analyticiterative scheme.

The inviscid limit of Navier-Stokes equations for locally near boundary analytic data on an exterior circular domain