Generalized variational principles for Boussinesq equation systems

Abstract

The semi-inverse method is proposed by He to establish the generalized variational principles for physical problems, which can eliminate variational crisis brought by the Lagrange multiplier method. Via the He s semi-inverse method, a family of variational principles is constructed for the Boussinesq equation systems and variant Boussinesq equation systems of fluid dynamics. The obtained variational principles have also proved to be correct.