Principle of minimum energy dissipation rate in steady Hele-Shaw flows

A new local form of the principle, in which dissipation is estimated only in a small vicinity of a free interface in steady Hele-Shaw flows, is proposed. It is established that for the problem of bubble propulsion the principle proposed is mathematically equivalent to the variational principle formulated by Saffman and Taylor without physical validation. It is shown that the new local form of the minimum dissipation principle effectively solves the problem of selection of a unique selection in the problems of both bubble and finger propulsion.