Grad(div(V)) = 0: Why is this Vector Identity Dropped?

[DoobleD]

This is closely related to this thread I posted yesterday, but the question is different so I created another thread. There is a vector identity often used when deriving EM waves equation :

Then the grad(div(V)) part of it is simply dropped, assuming it equals 0. And I wonder why.

Is it because, since there is no "sources" here (no charges), any divergence is 0 ? Can this be proven more formally ?

 

[Samy_A]

Isn't it because the identity is used for $V=E$ and $V=H$, and according to Maxwell's equations (see your Wikipedia link):
$\nabla.{E}=0$
$\nabla.{H}=0$
?

 

[haushofer]

Yes, that's the reason.

 

[DoobleD]

Isn't it because the identity is used for $V=E$ and $V=H$, and according to Maxwell's equations (see your Wikipedia link):
$\nabla.{E}=0$
$\nabla.{H}=0$
?

Oh ! Of course ! Thank you. Well, I formulated that divergence without charges/sources is 0, that is indeed Gauss's law from Maxwell's in vacuum...There is the obvious formalism I was looking for, I should have seen it. -_-'