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Solvability of control problems for stationary equations of magnetohydrodynamics of a viscous fluid. (Russian, English) Zbl 1050.35077
Sib. Mat. Zh. 45, No. 2, 243-263 (2004); translation in Sib. Math. J. 45, No. 2, 197-213 (2004).
The article is devoted to studying a boundary value problem for stationary equations of magnetohydrodynamics of a viscous incompressible fluid with inhomogeneous boundary conditions for velocity and electromagnetic field. Existence of a global generalized solution is proven under suitable assumptions on the data of the problem. Sufficient conditions for unique solvability of the problem are given. A control problem is analyzed for the boundary value problem. This involves proving existence of generalized solutions and studying an optimality system both for arbitrary and for concrete quality functionals.

35Q35 PDEs in connection with fluid mechanics
76W05 Magnetohydrodynamics and electrohydrodynamics
35B37 PDE in connection with control problems (MSC2000)
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