On symmetry group extension and vorticity conservation in Lagrangian continual systems

Abstract Examples of many Lagrangian hydrodynamic systems show that often in medium motion the conservation of the rotor of certain covector (e.g. medium velocity) takes place. The absence of initial vorticity of such a covector leads to the local reduction of the number of sought function and can be used for the construction of wide classes of “potential” solutions. It is shown that group nature of this conservation law corresponds to the invariance of the Lagrangian under equiaffine transformation group of independent variables. As application, the models of inhomogeneous incompressible fluid, adiabatic gas motion with varying entropy, magnetohydrodynamics, nonlinear theory of thermoelasticity are considered.