The traditional formulation of the boundary Crocco problem involves the dependence of a transfer coefficient on the density distribution of the concentration. In this case the boundary problem for the Crocco equation is associated with the condition of the minimum for a positive distribution, and the equation itself is equivalent to the canonical system of two equations. The possibility of immersion of flow of boundary problem in the field of extremals, monotony and convexity of the Crocco potential have been proved. In a number of physical problems, the distribution of the transfer coefficient depends on the flux density of conservative tracer, that is, on density gradient of concentration distribution. In this case, there are simple solutions of the boundary Crocco problem with a compact supporter. In other words, the solutions are grouped on a set of the finite measure.