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Perfect fluid flows over $$\mathbb{R}^n$$ with asymptotic conditions. (English) Zbl 0306.58007

##### MSC:
 58D05 Groups of diffeomorphisms and homeomorphisms as manifolds 35Q05 Euler-Poisson-Darboux equations 76G25 General aerodynamics and subsonic flows 76J20 Supersonic flows
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##### References:
 [1] Arnold, V, Sur la géométrie différentielle des groupes de Lie de dimension infinie et ses applications à l’hydrodynamique des fluids parfait, Ann. inst. Grenoble, 16, 1, 319-361, (1966) · Zbl 0148.45301 [2] Cantor, M, Global analysis over noncompact spaces, (), Chap. 2 · Zbl 0402.58004 [3] \scM. Cantor, Spaces of functions with asymptotic conditions on $$R$$^n, preprint. · Zbl 0441.46028 [4] Ebin, D; Marsden, J, Groups of diffeomorphisms and the motion of an incompressible fluid, Ann. of math., 92, 102-163, (1970) · Zbl 0211.57401 [5] Friedman, A, Partial differential equations, (), 19-31 [6] Kato, T, On classical solutions of the two-dimensional nonstationary Euler equation, Arch. rat. mech. anal., 25, 188-200, (1967) · Zbl 0166.45302 [7] Kato, T, Nonstationary flows of viscous and ideal fluids in $$R$$^3, J. functional analysis, 9, 296-305, (1972) · Zbl 0229.76018 [8] \scT. Kato, On the initial problem for quasi-linear symmetric hyperbolic systems, to appear. · Zbl 0343.35056 [9] Lang, S, Introduction to differentiable manifolds, (1962), Interscience NY · Zbl 0103.15101 [10] Lichtenstein, L; Lichtenstein, L; Lichtenstein, L; Lichtenstein, L; Lichtenstein, L; Lichtenstein, L, Über einge existenzproblem der hydrodynamik homogener unzusammendrückbarer, reibungsloser flüssigkeiter und die helmholtzschen wirbelsatze, Math. Z., Math. Z., Math. Z., Math. Z., Math. Z., Math. Z., 32, 608-415, (1930) · JFM 56.1249.01 [11] Marsden, J; Ebin, D; Fischer, A, Diffeomorphism groups, hydrodynamics, and relativity, (), 135-279 [12] Montgomery, D, On consinuity in topological groups, Bull. amer. math. soc., 42, 879, (1936) · JFM 62.1230.04 [13] Palais, R, Foundations of global nonlinear analysis, (1968), Benjamin NY · Zbl 0164.11102 [14] Swann, H.S.G, The convergence with vanishing viscosity of nonstationary Navier-Stokes flow to ideal flow in $$R$$^3, Trans. amer. math. soc., 157, 373-397, (1971) · Zbl 0218.76023
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