Additional conservation laws, functional relations between conservation laws, and potentials of divergent gas dynamics equations

The problems of constructing and revealing the functional relations between conservation laws, and constructing and finding additional conservation laws for the conservation laws previously obtained for three-dimensional unsteady flows (Terent’ev and Shmyglevskii, 1975), and for an infinite set of conservation laws for plane potential flows (Rylov, 2002), are considered. A functional relation means here that the sum of three or more left-hand sides of the divergent equations, with variable coefficients to be determined, is equal to zero.