Cb. Kim et Tj. Yang, LOWER-BOUND FOR TRANSPORT FOR PASSIVE ADVECTION, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 50(2), 1994, pp. 1668-1671
The lower bound for the passively advected flux is studied. It is comp
letely rigorous and turns out to be close to, or of the order of magni
tude of, the true value. The lower bound is obtained through the varia
tional principle which incorporates the physical constraints-i.e., the
conservation laws of the flux and the energy. It can be argued that t
he same method can be applied to a variety of problems with physical i
mplications.