Modified Lagrange multiplier method and generalized variational principle in fluid mechanics. (English) Zbl 0905.76066

Summary: The Lagrange multiplier method plays an important role in establishing generalized variational principles not only in fluid mechanics, but also in elasticity. Sometimes, however, one may come to a crisis (some multipliers vanish identically). This crisis is caused by the fact that the multipliers are treated as independent variables in the process of variation, but after identification they become functions of the original independent variables. To overcome it, we propose a modified Lagrange multiplier method or semi-inverse method to deduce generalized variational principles. Some examples are given to illustrate the effectiveness of the method.


76M30 Variational methods applied to problems in fluid mechanics
49S05 Variational principles of physics
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