Variational principles of the linear kinetic theory of a gas

Slow flows of a monatomic rarified gas which interacts with the surface of a solid according to a general law are considered. A functional is constructed, the Euler equations of which are linear kinetic equations with natural boundary conditions. The functional is the difference between the doubled power of the internal forces of the medium and the entropy production. The minimax nature of the extremum of the new functional is established.