Thanks to these vector identities, the incompressible Euler equations with constant and uniform density and without external field can be put in the so-called conservation (or Eulerian) differential form, with vector notation: { ∂ ∂ u ∂ ∂ t + ∇ ∇ ⋅ ⋅ ( u ⊗ ⊗ u + w I ) = 0 ∂ ∂ 0 ∂ ∂ t + ∇ ∇ ⋅ ⋅ u = 0 , or with Einstein notation: { ∂ ∂ t u j + ∂ ∂ i ( u i u j + w δ δ i j ) = 0 ∂ ∂ t 0 + ∂ ∂ j u j = 0 ,