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(E) dUJdt + DUt • Ut = -grad Pv div Ut = 0. T. Kato [4] and H. Swann [6] achieved similar results by showing that solutions to the Navier-Stokes equations for viscous flows converge to solutions of E in H = L?s as the viscosity approaches zero. Our results differ from theirs in that the solutions we establish possess a wider variety of asymptotic conditions at infinity. The proofs of the theorems shall appear elsewhere [1], [2]. Future work includes the extension of these results to flows over noncompact Riemannian manifolds and the study of the related problem of exterior flows in R. The author would like to thank J. Marsden and K. Uhlenbeck for their helpful advice.

Groups of diffeomorphisms of 𝑅ⁿ and the flow of a perfect fluid