Existence of solution of Rayleigh-type equation on semi-infinite cylinder with Coulomb-type potential

Abstract

In this paper we study a Rayleigh-type equation on a semi-infinite cylinder with a Coulomb-type potential. This equation arises in the double-deck boundary layer structure in the problem of flow induced by a uniformly rotating disk with small periodic irregularities on its surface for large Reynolds numbers. Using combined numerical and analytical approach, the existence of a unique solution to the Rayleigh-type equation is proven.