Can anyone check this identity please?

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SUMMARY

The discussion centers on verifying a vector calculus identity involving a scalar function and a vector function. The correct identity is stated as ∇ · (fV) = ∇f · V + f(∇ · V), where f is a scalar function and V is a vector function. The original query was incorrect as it lacked a necessary term, specifically v(Div(v)), which is zero in the context of fluid dynamics. The clarification provided resolves the misunderstanding and confirms the validity of the corrected identity.

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  • Familiarity with scalar and vector functions in mathematical physics.
  • Knowledge of fluid dynamics principles and their mathematical representations.
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Homework Statement



I just want to check if this identity is true, since I have not found it anywhere, can anyone help me?

v is a vector (and that nu is supposed to be a v too)
 

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The "identity" only makes sense if one of the factors is a scalar, and it's wrong even then. I think you want this, where f is a scalar function and V is a vector function:

\nabla \cdot f\vec V = \nabla f \cdot \vec V + f (\nabla \cdot \vec V)
 
I finally found it, looks like I was missing another term in the right side v(Div(v)), altough this is 0 in my case because I am working with fluid dynamics. Now everything makes perfect sense, thanks anyway
 

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