No abstract

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Without imposing the so-called compatibility condition on the initial data, we obtain an asymptotic expansion of the Stokes solutions at small viscosity ε as the sum of the linearized Euler solution and a corrector function, which balances the discrepancy on the boundary of the Stokes and the linearized Euler solutions. Using such an expansion and smallness of the corrector, as the viscosity ε tends to zero, we obtain the uniform L 2 convergence of the Stokes solutions to the linearized Euler solution with rate of order ε 1/4 .

The goal of this article is to study the asymptotic behaviour of the solutions of linearized Navier-Stokes equations (LNSE), when the viscosity is small, in a general (curved) bounded and smooth domain in R 3 with a characteristic boundary. To handle the difficulties due to the curvature of the boundary, we first introduce a curvilinear coordinate system which is adapted to the boundary. Then we prove the existence of a strong corrector for the LNSE. More precisely, we show that the solution of LNSE behaves like the corresponding Euler solution except in a thin region, near the boundary, where a certain heat solution is added as a corrector.