Geodesic
Properties of solutions of some extremal problems connected with the Navier--Stokes system
Sbornik. Mathematics, Tome 46 (1983) no. 3, pp. 323-351

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Properties of solutions of some control problems for a system described by the Navier–Stokes equations are studied with no restrictions on the control parameter. Necessary and sufficient conditions for an extremum are obtained, and the uniqueness and smoothness of solutions of control problems are investigated. The corresponding Euler–Lagrange equations are studied. Bibliography: 15 titles. 
@article{SM_1983_46_3_a1,
     author = {A. V. Fursikov},
     title = {Properties of solutions of some extremal problems connected with the {Navier--Stokes} system},
     journal = {Sbornik. Mathematics},
     pages = {323--351},
     publisher = {mathdoc},
     volume = {46},
     number = {3},
     year = {1983},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1983_46_3_a1/}
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A. V. Fursikov. Properties of solutions of some extremal problems connected with the Navier--Stokes system. Sbornik. Mathematics, Tome 46 (1983) no. 3, pp. 323-351. http://geodesic.mathdoc.fr/item/SM_1983_46_3_a1/