  We analyze, in two dimensions, an optimal control problem for the
Navier--Stokes equations where the control variable corresponds to the
amplitude of forces modeled as point sources; control constraints are also
considered. This particular setting leads to solutions to the state equation
exhibiting reduced regularity properties. We operate under the framework of
Muckenhoupt weights, Muckenhoupt-weighted Sobolev spaces, and the corresponding
weighted norm inequalities and derive the existence of optimal solutions and
first and, necessary and sufficient, second order optimality conditions.
