New conserved integrals and invariants of radial compressible flow in <i>n</i> &gt; 1 dimensions

Conserved integrals and invariants (advected scalars) are studied for the equations of radial compressible fluid/gas flow in n &gt; 1 dimensions. Apart from entropy, which is a well-known invariant, three additional found an explicit determination up to first order. One holds general equation state, two others hold only entropic state. A recursion operator on presented, produces hierarchies higher-order invariants. Each invariant yields corresponding integral describing advected conserved transported domains. In addition, direct kinematic densities uncovers ‘hidden’ non-advected integrals: one describes enthalpy-flux, holding barotropic state; other entropy-weighted energy, further class first-order shows that non-kinematic domains equivalent invariants, modulo trivial densities.