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

Using methods introduced by S. Schochet in J. Differential Equations 114 (1 994), 476-512, we compute the first term of an asymptotic expansion of the solutions of hyperbolic equations perturbated by a skew-symmetric linear op erator. That result is first applied to two systems describing the motion o f geophysic fluids: the rotating Euler equations and the primitive system o f the quasigeostrophic equations. Finally in the last part, we study the sl ightly compressible Euler equations by application of that same result. (C) 1998 Academic Press.