Can anyone check this identity please?

[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!

Div(VV)=v.(Grad(V))

 

[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})

 

[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 I am working with fluid mechanics.
Thanks again!

 

[hunt_mat]

Incompressible flow?

 

[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 :)