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We construct multisymplectic formulations of fluid dynamics using the inverseof the Lagrangian path map. This inverse map -- the ``back-to-labels'' map --gives the initial Lagrangian label of the fluid particle that currentlyoccupies each Eulerian position. Explicitly enforcing the condition that thefluid particles carry their labels with the flow in Hamilton's principle leadsto our multisymplectic formulation. We use the multisymplectic one-form toobtain conservation laws for energy, momentum and an infinite set ofconservation laws arising from the particle-relabelling symmetry and leading toKelvin's circulation theorem. We discuss how multisymplectic numericalintegrators naturally arise in this approach

Multisymplectic formulation of fluid dynamics using the inverse map