Differentical equations, dynamical systems and optimal control

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

R. K. Gaydukov

HSE University, ul. Myasnitskaya, 20, 101000, Moscow, Russia

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.

Keywords: existence and uniqueness of solution, Rayleigh-type equation, double-deck structure.

UDC: 517.95

MSC: 35A01

Received November 1, 2023, published March 13, 2024

DOI: 10.33048/semi.2024.21.012