EULER EQUATIONS IN A THIN SPHERICAL-SHELL

For the Euler equations in the thin domain bounded by the spheres of r adii 1 and 1 + epsilon, we show that if the initial datas are bounded in H-3 and epsilon-close in H-2 to two-dimensional data on the unit sp here S-2, then the classical solution of the Euler equations exists on a time interval [O, T (epsilon)], where T (epsilon) --> +infinity as epsilon --> O. Moreover, on this interval, we compare this solution wi th that of a system of limiting equations on S-2.