Geodesic
Distributed control of a heat conducting, time-dependent, Navier-Stokes fluid
Glasgow mathematical journal, Tome 44 (2002) no. 2, pp. 191-200

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The purpose of this paper is to study an optimal control problem associated with the thermally coupled Navier-Stokes equations. An existence result for this problem is obtained. The most important result of this paper is the proof of the existence and regularity of a solution of the adjoint system. By defining several functions, this system (which is not a divergence free one) is replaced by a divergence free system. 
Stavre, Ruxandra. Distributed control of a heat conducting, time-dependent, Navier-Stokes fluid. Glasgow mathematical journal, Tome 44 (2002) no. 2, pp. 191-200. doi: 10.1017/S0017089502020013
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     title = {Distributed control of a heat conducting, time-dependent, {Navier-Stokes} fluid},
     journal = {Glasgow mathematical journal},
     pages = {191--200},
     year = {2002},
     volume = {44},
     number = {2},
     doi = {10.1017/S0017089502020013},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089502020013/}
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