Problem #$2$

Verify the identity

${}_{\text{i}\text{j}\text{k}}{a}_{k,j}=2(w_l^{}+w_i{v}_{j,j}-w_j{v}_{i,j})$

And by using this identity as well as the results from Problem $5\mathrm{.}1,$ prove that the material derivative of the vorticity flux equation equals one half of the flux of the curl of the acceleration; that is$,$ show that $\frac{d}{dt}{\displaystyle \underset{a}{\overset{\phantom{}}{}}}{w}_i{n}_{i}da=\frac{1}{2}{\displaystyle \underset{a}{\overset{\phantom{}}{}}}{}_{\text{i}\text{j}\text{k}}{a}_{k,j}{n}_{i}da.$