In this paper, theorems on the existence of smooth solutions of certain control problems describable by the Navier-Stokes and Euler equations are proved. It is shown that a mixed boundary value problem for the Navier-Stokes and Euler equations of dimension is uniquely solvable for a dense set of right-hand sides.Bibliography: 13 titles.
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Andrei Vladimirovich Fursikov (1982) studied this question.