Proof - Vector Calculus - Curl

[cristina89]

I need to prove this: u x ($\nabla$ x u) = $\frac{1}{2}$$\nabla$(u²) - (u $\cdot$ $\nabla$)u.

I've came to this: uj∂iuj - uj∂jui (i think it's correct)
But how this 1/2 appears?

 

[tiny-tim]

welcome to pf!

hi cristina89! welcome to pf!

(try using the X₂ button just above the Reply box )

I need to prove this: u x ($\nabla$ x u) = $\frac{1}{2}$$\nabla$(u²) - (u $\cdot$ $\nabla$)u.

I've came to this: uj∂iuj - uj∂jui (i think it's correct)
But how this 1/2 appears?

'cos ∂_i(u_ju_j)= 2u_j∂_i(u_j)