Baev A.V.

Initial problems for the equations of motion of a viscous incompressible fluid and gas in Lagrangian variables are considered. It is shown that the motion of an incompressible fluid is not related to pressure. The pressure in the absence of external forces is constant, what allows the fluid to move freely. This motion is purely vortex in nature and is described by quasi-linear equations of the parabolic type. The existence and uniqueness of the classical periodic solution of the initial problem in Rn at n > 2 is proved. The equations of motion of liquid and gas in steady-state mode are obtained. The problem of turbulent flow of partially compressible liquid and gas is solved. It is established that there is no turbulent flow in an incompressible fluid. It is shown that as a result of frequency synchronization, spatially stable periodic structures arise.

The concept of steady-state solutions of the Navier–Stokes equation is defined. Such solutions expand the concept of stationary, exponentially decrease in time, have a constant spatial velocity field and constant pressure in the absence of external fields. The method of their construction is considered, and the problem of Taylor vortices is solved. A mathematical model of a tornado is proposed. Within the framework of this model, a steady-state solution is obtained as an eigenfunction of the problem in the form of a vortex. Based on the Navier–Stokes equation, a model of the formation of the structure of a gas cloud is proposed. It is shown that due to the Coriolis force, spiral arms arise from flows of gas moving outward. It is proved that the number of arms m is even, and their structure does not depend on the angular velocity of rotation. A formula is obtained for the spiral twist angle depending on the cloud parameters for the case of m=2.