Geodesic
Sixth problem of the millennium: Navier--Stokes equations, existence and smoothness
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 58 (2003) no. 2, pp. 251-286

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This paper presents the main results concerning solubility of the basic initial-boundary value problem and the Cauchy problem for the three-dimensional non-stationary Navier–Stokes equations, together with a list of what to prove in order to solve the sixth problem of the “seven problems of the millennium” proposed on the Internet at the site http://claymath.org/. 
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     author = {O. A. Ladyzhenskaya},
     title = {Sixth problem of the millennium: {Navier--Stokes} equations, existence and smoothness},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
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     number = {2},
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     url = {http://geodesic.mathdoc.fr/item/RM_2003_58_2_a1/}
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O. A. Ladyzhenskaya. Sixth problem of the millennium: Navier--Stokes equations, existence and smoothness. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 58 (2003) no. 2, pp. 251-286. http://geodesic.mathdoc.fr/item/RM_2003_58_2_a1/