Non-relativistic conformal symmetries in fluid mechanics

Understand

The symmetries of a free incompressible fluid span the Galilei group, augmented with independent dilations of space and time.

• When the fluid is compressible, the symmetry is enlarged to the expanded Schroedinger group, which also involves, in addition, Schroedinger expansions.
• While incompressible fluid dynamics can be derived as an appropriate non-relativistic limit of a conformally-invariant relativistic theory, the recently discussed Conformal Galilei group, obtained by contraction from the relativistic conformal group, is not a symmetry.
• This is explained by the subtleties of the non-relativistic limit.