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The Euler Equations on Thin Domains

By Jerrold E. Marsden, Tudor S. Ratiu and Geneviève Raugel


For the Euler equations in a thin domain Qε =Ω×(0,ε), Ω a rectangle in R 2, with initial data in (W 2,q (Qε)) 3, q>3, bounded uniformly in ε, the classical solution is shown to exist on a time interval (0,T(ε)), where T(ɛ) → + ∞ as ɛ → 0. We compare this solution with that of a system of limiting equations on Ω.

Year: 2009
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