On the construction of boundary layers in the incompressible limit with boundary

Abstract

In this paper we give a more precise construction of the boundary layer used to prove the strong decay of the acoustic waves in the paper [4]. Indeed, the construction in [4] is not completely correct in the case when eigenvalues are not simple and some additional conditions should be imposed on the basis of eigenvectors chosen. There is an extra interesting algebraic structure based on a sequence of symmetric operators that should be used in this choice. This construction can be extended to the case of Robin boundary condition as well as to the full acoustic operator which includes the heat conductivity effect. Moreover, this paper allows us to extend the construction of the viscous boundary layer in the hydrodynamic limit of the Boltzmann equation used in our paper [7] to the general case.