Abstract

Application of Lie Symmetry Analysis to Gas- and Hydrodynamics

A.Chupakhin (Lavrentyev Institute of Hydrodynamics, Novosibirsk, Russia)

e-mail: chupakhin@hydro.nsc.ru

We consider systematical application of Lie-Ovsyannikov group analysis of differential equations to hydro- and gas dynamics problems and new original approaches. --Classification of SO(3)-partially invariant solutions of gas dynamics equations. Integration of invariant submodels of this model. The special property of the Jacobi matrix of velocity vector field in this model: algebraic invariants depend only on invariant independent variables. --Differential invariant vectors and tensors. The new possibilities for construction exact solutions of differential equations. These questions are discussed and illustrated by many examples.

Section : 12