Well actually -
Since the real flow processes are probabilistic (some molecules will go thisaway, some thataway) it is feasible to design a computer program to model several different molecular scenarios, and then match up a mix of these with empirical data.
I believe that's what CFD (computational flow dynamics) programs do. Certainly not a "neat elegant mathematical treatment" in the sense of a single equation to solve, but it's possible to "thrash the problem to death" via computer.