Boundary Layers for the Navier-Stokes Equation : the case of characteristic boundary

Abstract. We prove the existence of a strong corrector for the linearized in-compressible Navier–Stokes solution on a domain with characteristic bound-ary. This case is different from the noncharacteristic case considered in [7] and somehow physically more relevant. More precisely, we show that the linearized Navier–Stokes solutions behave like the Euler solutions except in a thin region, close to the boundary, where a certain heat equation solution is added (the corrector). Here, the Navier–Stokes equations are considered in an infinite channel of R3 but our results still hold for more general bounded domains