Orthogonality Relations for a Stationary Flow of an Ideal Fluid

Abstract

For a real solution (u, p) to the Euler stationary equations for an ideal fluid, we derive an infinite series of the orthogonality relations that equate some linear combinations of mth degree integral momenta of the functions u_iu_j and p to zero (m = 0, 1,... ). In particular, the zeroth degree orthogonality relations state that the components ui of the velocity field are L²-orthogonal to each other and have coincident L²-norms. Orthogonality relations of degree m are valid for a solution belonging to a weighted Sobolev space with the weight depending on m.