First, the following identities hold: ∇ ∇ ⋅ ⋅ ( w I ) = I ⋅ ⋅ ∇ ∇ w + w ∇ ∇ ⋅ ⋅ I = ∇ ∇ w u ⋅ ⋅ ∇ ∇ ⋅ ⋅ u = ∇ ∇ ⋅ ⋅ ( u ⊗ ⊗ u ) where ⊗ ⊗ denotes the outer product. The same identities expressed in Einstein notation are: ∂ ∂ i ( w δ δ i j ) = δ δ i j ∂ ∂ i w + w ∂ ∂ i δ δ i j = δ δ i j ∂ ∂ i w = ∂ ∂ j w u j ∂ ∂ i u i = ∂ ∂ i ( u i u j ) where I is the identity matrix with dimension N and δ ij its general element, the Kroenecker delta.