# Can anyone check this identity please?

1. Sep 7, 2011

### Deathcrush

is this identity true?

V is a vector, so VV is a second order tensor

I have tried to prove this but the components of the tensor appear always as operands of the nabla.

Thanks!

2. Sep 9, 2011

### hunt_mat

The way to go about proving this is to write $V\otimes V=V_{i}V_{j}$ and write the divergence as $\partial^{i}(V_{i}V_{j})$

3. Sep 9, 2011

### Deathcrush

I know now, thank you. Actually that "identity" es not true unless Div(v)=0, because another term is missing. However that fits perfectly since im working with fluid mechanics.
Thanks again!

4. Sep 10, 2011

### hunt_mat

Incompressible flow?

5. Sep 10, 2011

### Deathcrush

yes, actually, I was trying to take the curl of the Navier-Stokes equation, to get the vorticity equation, a problem in Bird's transport phenomena, the book asks you to deduce it in two forms, the first one is the one I have already, the second one involves the Levi-Civita symbol and I'm currently working on it :)