Maximum principle in the boundary control problem for flow of a viscous fluid (Q1335974)

We consider the control problem for the Navier-Stokes evolution equations that describe the flow of a viscous incompressible fluid in an unbounded domain \(\Omega\subset \mathbb{R}^ d\), \(d=2,3\). This problem can be interpreted as a problem of minimizing the flow through the segment \(\Gamma\subset \partial\Omega\) under restrictions on the flow head on the boundary. The singular optimality system for the considered problem is obtained in the form of an analogue of the Pontryagin maximum principle; moreover, for two-dimensional flows we impose no additional conditions like smallness or regularity.