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Euler evolution for singular initial data and vortex theory. (English) Zbl 0529.76023

MSC:
76B47 Vortex flows for incompressible inviscid fluids
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[1] Helmholtz, H.: On integrals of hydrodynamical equations which express vortex-motion. Philos. Mag.33, 485 (1867)
[2] Kirchoff, G.R.: Vorlesungen über Math. Phys., Vol. I. Leipzig: Teubner 1876
[3] Poincaré, H.: Theorie des turbillons. Paris: G. Carré 1893
[4] Hald, O., Mauceri Del Prete, V. v.: Convergence of vortex methods for Euler’s equations. Math. Comp.32, 791 (1978) · Zbl 0387.76021
[5] Hald, O.: The convergence of vortex methods. II. SIAM J. Numer. Anal.16, 726 (1979) · Zbl 0427.76024 · doi:10.1137/0716055
[6] Marchioro, C., Pulvirenti, M.: Hydrodynamics in two-dimensions and vortex theory. Commun. Math. Phys.84, 483 (1982) · Zbl 0527.76021 · doi:10.1007/BF01209630
[7] Beale, J.T., Majda, A.: Vortex methods. I. Convergence in three-dimensions. Math. Comp.39, 1 (1982); Vortex methods. II. Higher order accuracy in two- and three-dimensions39, 29 (1982)
[8] Marchioro, C., Pulvirenti, M.: Vortex methods in two-dimensional fluid dynamics (in preparation) (1983) · Zbl 0551.70005
[9] Aref, H.: Motion of three vortices. Phys. Fluids22, 393 (1979) · Zbl 0394.76025 · doi:10.1063/1.862605
[10] Dürr, D., Pulvirenti, M.: On the vortex flow in bounded domains. Commun. Math. Phys.85, 256 (1982)
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