Asymptotic of the Solutions of Hyperbolic Equations with a Skew-Symmetric Perturbation

Using methods introduced by S. Schochet inJ. Differential Equations114(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.