More specifically: I was reading on how physically correct solutions to the frictionless Burgers equation are constructed when a shock appears as "weak solutions" of the general equation in the limit of vanishing viscosity. Entropy is then only generated at the shocks and searching for a solution which minimizes entropy production leads to the correct result. In easy two dimensional air foil problems one only has to fix the value of rotational flow. I wonder whether this can not also be reduced to a problem of minimizing entropy.
In the inviscid flow the velocity becomes infinite at a sharp trailing edge for almost all values of the rotation. If a small viscosity is introduced, velocity is no longer infinite but there would probably a lot of entropy be generated.