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Properties of solutions of some extremal problems connected with the Navier–Stokes system

A. V. Fursikov


Abstract: 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.

UDC: 517.946

MSC: 35Q10, 76D05, 49A22, 49B22

Received: 30.07.1981

 English version: Mathematics of the USSR-Sbornik, 1983, 46:3, 323–351

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