On the solutions of Cauchy problem for quasi-hydrodynamic system

The coincidence of bounded in space at arbitrary instant of time homogeneously screw infinitely differentiable solutions of the Cauchy problem for quasi-hydrodynamic system and Navier-Stokes system is proved. It is shown that any smooth solution of Cauchy problem for Navier-Stokes system that obeys the generalized Gromeki-Beltrami condition, as well as some boundedness conditions in space, satisfies to quasi-hydrodynamic system. Examples of solutions are given. The formulation of an unsolved problem is given, in which it is required to prove the existence and uniqueness of a smooth solution of Cauchy problem for the quasi-hydrodynamic system.