Existence of the First Integral in a Problem of Optimally-Controlled BL Theory

The paper states the problem of minimizing the integral drag of friction in the presence of restrictions preset on the control system power. As the control, a specific flow rate of liquid is used here, injected into the basic flow through the porous or perforated section of the surface streamlined. This problem can be related to the class of Meyer's variation problems with two independent variables. It is significant here that the corresponding conservation law for conjugate system of equations transforms automatically into the first integral to be valid at any velocity on the outer BL border and at any Prandtl numbers chosen.