Can anyone check this identity please?

  • Thread starter Deathcrush
  • Start date
40
0
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

Homework Helper
1,686
12
The way to go about proving this is to write [itex]V\otimes V=V_{i}V_{j}[/itex] and write the divergence as [itex]\partial^{i}(V_{i}V_{j})[/itex]
 
40
0
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!
 

hunt_mat

Homework Helper
1,686
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Incompressible flow?
 
40
0
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 :)
 

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