Tensor invariants of dynamical systems and steady viscous flows (Q1405937)

The author studies the problem on randomness of stationary flows of a viscous liquid. Two models are considered: a barotropic compressible viscous liquid and an incompressible ideal liquid with external friction. By means of the well-known Poincaré theorem [\textit{H. Poincaré}, ``Selected papers in three volumes''. Vol. 1: New methods of celestial mechanics, Nauka, Moscow (1971; Zbl 0232.01018)] it is shown that the typical stationary flows of liquid (in the above mentioned models) are chaotic: they do not admit non-trivial integrals, fields of symmetry and integral invariants.