Conjugate flow action functionals
- Division of Applied Mathematics, Brown University, Rhode Island 02912 (United States)
We present a new general framework to construct an action functional for a non-potential field theory. The key idea relies on representing the governing equations relative to a diffeomorphic flow of curvilinear coordinates which is assumed to be functionally dependent on the solution field. Such flow, which will be called the conjugate flow, evolves in space and time similarly to a physical fluid flow of classical mechanics and it can be selected in order to symmetrize the Gâteaux derivative of the field equations with respect to suitable local bilinear forms. This is equivalent to requiring that the governing equations of the field theory can be derived from a principle of stationary action on a Lie group manifold. By using a general operator framework, we obtain the determining equations of such manifold and the corresponding conjugate flow action functional. In particular, we study scalar and vector field theories governed by second-order nonlinear partial differential equations. The identification of transformation groups leaving the conjugate flow action functional invariant could lead to the discovery of new conservation laws in fluid dynamics and other disciplines.
- OSTI ID:
- 22251914
- Journal Information:
- Journal of Mathematical Physics, Vol. 54, Issue 11; Other Information: (c) 2013 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
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