Vortices in the Prandtl boundary layer induced by irregularities on a plate

Existence of the stationary solution of a Rayleigh-type equation

“…We note that the results of this paper (see Theorem 2) together with the results in [1] prove that the stationary solution of the Rayleigh-type equation (2.2) exists and is unique for all x > δ and δ > 0 (i.e., in the entire region under study) and this fact actually means the existence of the double-deck structure (because all equations describing this structure are solvable).…”

“…In [1] we proved that the stationary solution of the Rayleigh-type equation (1.8), (1.9) exists for all x > M (x is the distance from the edge of the plate), where…”

“…In this paper, we continue our study of the Rayleigh-type equation (1.8), which was started in [1]; see also [2]. It is known that the Rayleigh equation (see [3]) plays an important role in fluid mechanics problems; see [4].…”

“…In [1], it was proved that the stationary solution of the Rayleigh-type equation (1.8) exists and is unique for all x > δ and δ > M, where x is the distance from the edge of the plate and M is a constant; see (2.1). The aim of this paper is to prove that a stationary solution of the Rayleigh-type equation (1.8) exists and is unique for all x > δ and δ ∈ (0, M] (i.e., at the edge of the plate).…”

“…In this section, we present the main results from [1,2], which we need for further discussion. We assume that the plate surface is described by the relation…”