Je. Marsden et al., EULER EQUATIONS IN A THIN SPHERICAL-SHELL, Comptes rendus de l'Academie des sciences. Serie 1, Mathematique, 321(9), 1995, pp. 1201-1206
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.