Checking a vector identity with v and ν

[Deathcrush]

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)

 

[LCKurtz]

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:

$$\nabla \cdot f\vec V = \nabla f \cdot \vec V + f (\nabla \cdot \vec V)$$

 

[Deathcrush]

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