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The dual least action problem for an ideal, incompressible fluid. (English) Zbl 0797.76006
It is shown that the weak least action problem describing the motion of an ideal incompressible fluid has a unique dual solution. Physically speaking, the dual solution is the pressure field governing the motion of the ideal incompressible fluid. The existence and uniqueness results suggest that the pressure field is a relevant unknown in the least action problem, rather than the flow field. The proof is based on the concept of ‘slightly compressible’ generalized flow and uses some results on the measure-preserving diffeomorphisms.

MSC:
76B99 Incompressible inviscid fluids
76M30 Variational methods applied to problems in fluid mechanics
58D30 Applications of manifolds of mappings to the sciences
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