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The article presents a new class of exact solutions to the system of Navier–Stokes equations, which allows one to take into account the nonlinear distribution of the pressure field and the influ-ence of external volumetric forces, as well as the possibility of horizontal fluid outflow/inflow when modeling its vertical motion. This class is a generalization of the Lin–Sidorov–Aristov class, which assumes the linear distribution of two projections of the fluid flow velocity vector along a part of the coordinates and the independence of the third projection of the velocity vector from these coor-dinates.

A class of exact solutions with spatial acceleration for the description of viscous incompressible fluid flows in the field of mass forces