Asymptotic of the solutions of hyperbolic equations with a skew-symmetric perturbation

Using methods introduced by S. Schochet in J. Differential Equations 114 (1994), 476-512, we compute the first term of an asymptotic expansion of the solutions of hyperbolic equations perturbated by a skew-symmetric linear operator. That result is first applied to two systems describing the motion of geophysic fluids: the rotating Euler equations and the primitive system of the quasigeostrophic equations. Finally in the last part, we study the slightly compressible Euler equations by application of that same result. (C) 1998 Academic Press.