Generalized variational principles of the Benney-Lin equation arising in fluid dynamics

Variational principle is important since it can not only reveal the possible solution structures of the equation but also provide the conservation laws in an energy form. Unfortunately, not all the differential equations can find their variational forms. In this work, the Benney-Lin equation is studied and its two different generalized variational principles are successfully established by using the semi-inverse method. The derivation process is given in detail. The finding in this work is expected to give a insight into the study of the nonlinear partial differential equations arising in fluid dynamics.

A short remark on Stewart 1962 variational principle for laminar flow in a uniform duct

This paper concludes that Stewart 1962 variational principle for laminar flow in a uniform duct is for a differential-difference. Some generalized variational principles are elucidated with or without Stewart?s discrete treatment.