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Can anyone check this identity please?

  1. Sep 7, 2011 #1
    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))
     
  2. jcsd
  3. Sep 9, 2011 #2

    hunt_mat

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    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]
     
  4. Sep 9, 2011 #3
    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!
     
  5. Sep 10, 2011 #4

    hunt_mat

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    Incompressible flow?
     
  6. Sep 10, 2011 #5
    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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