On the construction of exact solutions of two-dimensional quasi-hydrodynamic system

New methods for constructing exact solutions of the quasi-hydrodynamic system for two-dimensional flows are proposed. It is shown that with any smooth solution of some overdetermined system of partial differential equations one can associate common exact solution of the quasi-hydrodynamic system and the Navier-Stokes system. Any eigenfunction of the two-dimensional Laplace operator also generates common solution to these systems. Examples of solutions are given in both the non-stationary and stationary cases. The principle of superposition of the fluid velocity vector fields for specific flows is discussed.