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On the Euler equations with a singular external velocity field. (English) Zbl 0714.76028
Summary: We study the Euler equations for an incompressible fluid in presence of a singular external velocity field produced by fixed point vortices. We prove the existence and the uniqueness of the solution.

MSC:
76B47 Vortex flows for incompressible inviscid fluids
35Q30 Navier-Stokes equations
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References:
[1] T. Kato , Arch. Rat. Mech. An. , 25 ( 1967 ), p. 95 . MR 211057
[2] C. Marchioro , Euler evolution for singular initial data and vortex theory : global solution , Commun. Math. Phys. , 116 ( 1988 ), pp. 45 - 55 . Article | MR 937359 | Zbl 0654.76017 · Zbl 0654.76017
[3] C. Marchioro , On the vanishing viscosity limit for two dimensional Navier-Stokes equations with singular initial data , Math. Meth. Appl. Sci . (in press). MR 1058150 | Zbl 0703.76020 · Zbl 0703.76020
[4] C. Marchioro - E. PAGANI, Evolution of two concentrated vortices in a two-dimensional bounded domain , Math. Meth. Appl. Sci. , 8 ( 1986 ), pp. 328 - 344 . MR 859828 | Zbl 0609.76019 · Zbl 0609.76019
[5] C. Marchioro - M. PULVIRENTI, Euler evolution for singular initial data and vortex theory , Commun. Math. Phys. , 91 ( 1983 ), p. 563 - 572 . Article | MR 727203 | Zbl 0529.76023 · Zbl 0529.76023
[6] C. Marchioro - M. Pulvirenti , Vortex methods in two-dimensional fluid mechanics , Lecture Notes in Physics , 203 , Springer , Heidelberg ( 1984 ). MR 750980 | Zbl 0545.76027 · Zbl 0545.76027
[7] C. Marchioro - M. Pulvirenti , Mechanics, Analysis and Geometry: 200 years after Lagrange , M. FRANCAVIGLIA & D. D. HOLM (eds.) North Holland (in preparation). MR 1098508 | Zbl 0714.00021 · Zbl 0714.00021
[8] B. Turkington , On the evolution of a concentrated vortex in an ideal fluid , Arch. Rat. Mech. An. , 97 ( 1987 ), pp. 75 - 87 . MR 856310 | Zbl 0623.76013 · Zbl 0623.76013
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