Lagrangian formulation of noncommutative fluid models

In this work we study Lagrangian formulations for the noncommutative versions of the irrotational and rotational fluid models. These formulations will be obtained by using the Faddeev–Jackiw symplectic formalism. In this context, interesting results will be revealed, for example, a chiral behavior into both fluid models comes up. In fact, distinct and non-dynamically equivalent Lagrangian descriptions of the noncommutative versions of the fluid models can be proposed.