Abstract |

**On Symmetry Group Extension and
Vorticity Conservation in Continuum Mechanics**

*A.Golubiatnikov (Faculty of Mechanics
and Mathematics,Moscow State University, Moscow, Russia)*

*e-mail:
golubiat@mech.math.msu.su*

Examples
of many Lagrange's hydrodynamic systems show that often in medium motion the
conservation of the curl of certain covector takes place. Moreover this
covector can be unequal to the medium velocity. The absence of initial
vorticity of such covector leads to the local reduction of the number of sought
function and can be used for construction of wide classes of
"potential" solution. It is
shown that group nature of this conservation law corresponds to the invariance
of the Lagrangian with respect to equiaffine (volume-preserving) transformation
group of independent Lagrange variables. In general case the Lagrange function
can be always reduced to such form by a special extension of sought function
set, moreover without presence of unnecessary information. As applications, the models of inhomogeneous
incompressible fluid, adiabatic motion of gas with varying entropy, magnetic
hydrodynamics, nonlinear theory of elasticity and some other media are
considered. Some exact solutions, having such potentiality properties, are also
presented. This work is supported by the
RFBR (grant 02-01-00613).

Section
: 12