A possibility of realizing the Landau—Hopf scenario in the problem of tube oscillations under the action of a fluid flow

Abstract

We consider a boundary-value problem for a quasilinear partial differential equation describing tube oscillations under the action of a fluid flow. We show that the well-known Landau—Hopf scenario of transition to turbulence is realized in the considered evolution boundary-value problem with a suitable choice of the governing parameter. To study the problem, we use the theory of infinite-dimensional dynamical systems. In particular, we use the method of integral manifolds, normal forms, and also asymptotic methods of analysis.