Higher-order Navier-Stokes type equations and non-linear problems of hydrodynamics

A higher-order gradient type vector in Cartesian coordinates was introduced. Navier-Stokes type equations containing this vector and the generalized Laplace operator are considered. Generalized curvilinear coordinates are introduced, and higher-order Navier-Stokes type equations in these coordinates has been proposed. A function describing the flow of the viscous liquid between two concentric non-circular cylinders is derived. The non-linear problem of the free surface of a liquid in a rotating non-circular cylinder is considered.