Boundary layers for the Navier-Stokes equations. The case of a characteristic boundary. (English) Zbl 1157.35333

Summary: We prove the existence of a strong corrector for the linearized incompressible Navier-Stokes solution on a domain with characteristic boundary. 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 \(\mathbb R^{3}\) but our results still hold for more general bounded domains.


35C20 Asymptotic expansions of solutions to PDEs
35K05 Heat equation
76D05 Navier-Stokes equations for incompressible viscous fluids
35B25 Singular perturbations in context of PDEs
35R30 Inverse problems for PDEs