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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.

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