Équations d'Euler dans une coque sphérique mince (Euler equations on a thin spherical shell)

Marsden, J. E., T. S. Ratiu and G. Raugel

C. R. Acad. Sci. Paris, 321, (1995), 1201-1206

Abstract:

For the Euler equations in the thin domain bounded by the spheres of radii 1 and 1 + $\varepsilon$ , we show that if the initial dates are bounded in H³ and $\varepsilon$ -close in H² to two-dimensional data on the unit sphere S² , then the classical solution of the Euler equations exists on a time interval [0, T($\varepsilon$)] , where T($\varepsilon$)$\to$ + $\infty$ as $\varepsilon$$\to$ 0 . Moreover, on this interval, we compare this solution with that of a system of limiting equations on S² .