Differentiation of functionals with variables coupled by constraints: Analysis through a fluid-dynamical model

Abstract

Analysing an application in liquid film dynamics, a guide for obtaining the corresponding constrained functional derivatives for constraints coupling the functional variables is given. The use of constrained derivatives makes the proper account for constraints possible in time-dependent, nonequilibrium physical theories, with physical equations not emerging as Euler-Lagrange equations, which is especially relevant with respect to the dynamics of complex liquids.