Inhomogeneous isobaric Poiseuille-Ekman flow of a viscous incompressible fluid

An analytical solution describing the stationary isobaric flow of a viscous incompressible slowly rotating fluid in an infinitely extended layer is obtained, with inhomogeneous velocity distribution. The fluid flow is considered at constant pressure, in accordance with the generalization of the classical Ekman flow. The allowance made for velocity gradients can both increase and decrease the number of stagnation points in the fluid layer as compared to the homogeneous Ekman flow. It is shown that the new exact solution allows us to construct new classes of exact solutions of the Navier-Stokes equations describing fluid flow in an inertial coordinate system and in a rotating one.