Exact Solutions of Incompressible Navier–Stokes Equations in the Case of Oil and Gas Industrial Problems

Classes of exact solutions corresponding to vortex and potential flows are presented within the framework of a hydrodynamic model describing flows of a viscous incompressible fluid. The study of exact solutions is a prerequisite for creating a core simulator, which is associated with modeling fluid dynamics in a porous medium and the response of the field to dynamic influences in order to increase oil recovery.