On the construction of boundary layers in the incompressible limit with boundary
This paper is an extension of the work by \textit{B. Desjardins} et al. [J. Math. Pures Appl., IX. Sér. 78, No. 5, 461--471 (1999; Zbl 0992.35067)]. There the authors constructed a boundary layer that was used as a test function like in the so-called method of oscillating test functions. But this construction presents a gap when the eigenvalues of the Laplacian with Neumann boundary conditions are not simple. The authors consider full acoustic and diffusion operators including the heat conductivity effect, which generates some new phenomena different from the isentropic case. This approach can be used to extend the construction of viscous boundary layers used in the hydrodynamic limit of the Boltzmann equation to the general case. Because of the additional dissipation effect from the heat conductivity, in the non-isentropic case considered, the authors are able to omit a geometric condition related to Schiffer's conjecture.
scientific article; zbMATH DE number 6374919