Applications of the differential invariants of infinite dimensional groups in hydrodynamics

Abstract

The bases of differential invariants for infinite-dimensional Lie groups, admitted by the Navier–Stokes and gas dynamics equations, are calculated. The possibilities of bases application to construct differentially invariant solutions are shown. In the terms of differential invariants the group interpretations of Karman’s solution, describing a liquid flow between rotating disks, and solution, giving a stationary cylindrical vortex in a viscous fluid, are given. The application of the bases of differential invariants to construct the group stratification of equations is shown by two examples. The examples are the group stratification for the stationary gas dynamics and for the transonic gas motion equations. The possibilities of group stratification use to form new group-invariant solutions are analyzed.