Acoustic model of zero-width slits and hydrodynamic boundary layer stability

The flow of a fluid in a two-dimensional half-space with a system of acoustic resonators joined to its boundary is investigated. The acoustic system is calculated using a model of zero-width slits based on the theory of self-adjoint extensions of symmetric operators. The influence of the acoustic effects on the stability of a boundary layer of viscous compressible fluid is taken into account. It is shown that for a definite choice of the parameters of the system it is possible to increase the critical Reynolds number, i.e., to laminarize the flow.