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Zero viscosity limit for analytic solutions of the Navier-Stokes equation on a half-space. II: Construction of the Navier-Stokes solution. (English) Zbl 0913.35103

[For part I see ibid., 433-461 (1998; reviewed above).]
In this second part of the paper, the authors investigate the zero-viscosity limit for the incompressible Navier-Stokes equations in a half space in bi- and tri-dimensional cases under the condition of analytic initial data. The construction of a solution to the Navier-Stokes system is the principal result. The solution is given as a composite asymptotic expansion involving the solutions of the Euler and Prandtl equations, found in the first part of the paper, plus an error term, written as sum of first-order Euler and Prandtl corrections, plus a further error term. All the paper is devoted to the analysis of the interplay of these parts of the general solution, the relation between the general solution and all its components and the behaviour of the solution in different domains of the flow. The whole paper is a minute analysis of the studied problem, made at a high mathematical level.

MSC:

35Q30 Navier-Stokes equations
35A10 Cauchy-Kovalevskaya theorems
35C20 Asymptotic expansions of solutions to PDEs

Citations:

Zbl 0913.35102
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