Nonlinear dynamics in the initial-boundary value problem on the fluid flow from a ledge for the hydrodynamic approximation to the boltzmann equations

We numerically analyze the laminar-turbulent transition in the problem on the flow of a viscous incompressible fluid from a ledge. To model the fluid flow, we use the Boltzmann integro-differential equations expanded in the Knudsen number. For the fundamental analysis, we use a numerical method of increased accuracy for the integration of the initial-boundary value problem. By analyzing the phase portraits of the behavior of the system, we find that the transition from a stationary solution to an irregular chaotic one takes place in accordance with the Feigenbaum-Sharkovskii-Magnitskii scenario. Moreover, the transition process differs from the results obtained by using the Navier-Stokes equations for solving a similar initial-boundary value problem.