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

Hamouda, Makram; Temam, Roger

Georgian Math. J. 15, No. 3, 517-530 (2008).

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.

MSC:

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

Keywords:

asymptotic expansions; boundary layer theory; heat equation; Navier-Stokes equations; singular perturbations; linearized incompressible Navier-Stokes solution; infinite channel of \(\mathbb R^{3}\)