Abstract

Basis of Differential Invariants for Several Concrete Groups and Its Applications

S.Golovin (Lavrentyev Institute of Hydrodynamics, Novosibirsk, Russia)

e-mail: sergey@hydro.nsc.ru

It is well known that many of the mathematical models admit infinite dimensional Lie group of transformations. That are, for example, Navier-Stokes and Euler equations, stationary gas dynamics equations, boundary layer Prandtl equations and others. Basis of differential invariants for infinite dimensional group gives the significant information about its structure. In present work basis of differential invariants for several mathematical models were constructed. For Navier-Stokes equations, describing three-dimensional motions of viscous fluid, basis consists of one finite and 12 first-order differential invariants. For the Navier-Stokes equations in presence of rotational symmetry basis includes in addition to finite, one first- and one second-order differential invariants. At last, description of basis of differential invariants for Munk-Prime transformation of stationary gas dynamics equations requires only one differential invariant of the first order. An application of the basis of differential invariants allows one to give a group treatment of known solution of above-mentioned models as well as to obtain a new one. Applications of basis of differential invariants to construction of group stratification are discussed.

Section : 12