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Published 2000 | Submitted
Book Section - Chapter Open

The Euler Equations on Thin Domains

Abstract

For the Euler equations in a thin domain Q_ε = 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(є) → +∞ as є → 0. We compare this solution with that of a system of limiting equations on Ω.

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© 2000, World Scientific

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August 19, 2023
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