The purpose of the work is the study of the laws of the dynamics of a viscous liquid undergoing periodic influences possessing no predominant direction in space under the presence and under the absence of gravity.

The methods. Analytical methods of the research of boundary problems for the equation of Navier–Stokes are used.

The results. A new problem on a viscous liquid motion under non-stationary influences is formulated and solved. The hydro-mechanical system consists of a viscous liquid and two solid bodies that are a curvilinear wall and a curvilinear membrane which is permeable for the liquid. The wall is at rest. The membrane fulfils a prescribed periodical motion. A homogeneous stationary gravity presents (or is absent). New effects of an average motion, new peculiarities of the viscous liquid dynamics are revealed.

The conclusion. The obtained results can be used in particular in a scientific search of original methods of a control hydro-mechanical systems.