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All the symmetries and conservation laws of Navier-Stokes equations are calculated.

This paper is devoted to differential invariants of equations y = a 3 (x, y)y 3 + a 2 (x, y)y 2 + a 1 (x, y)y + a 0 (x, y).w.r.t. point transformations. The natural bundle of these equations and its bundles of kjets of sections, k = 0, 1, 2, . . . , are considered. The action of the pseudogroup of all point transformations on these bundles is investigated. Tensor differential invariants distinguishing orbits of this action on jet bundles of second and third orders are constructed. A complete collection of generators and their differential syzygies is obtained for the algebra of all scalar differential invariants of a wide class of considered equations containing generic equations.

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Abstract. In this paper basic differential invariants of generic hyperbolic Monge-Ampère equations with respect to contact transformations are constructed and the equivalence problem for these equations is solved.