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A Lax representation, symmetries, and conservation laws for the three-dimensional Euler--Helmholtz equations
We consider the three-dimensional Euler--Helmholtz equations for an inviscid incompressible fluid. Under the Poincar{é} lemma assumption, the incompressibility condition is resolved by introducing a vector potential, leading to a vorticity-type reformulation of the system. The main result is the con
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