What's the definition of $\operatorname{div}(u\otimes u)$?

Question

I've found the symbol sequence $\operatorname{div}(u\otimes u)$ in a PDE. What is $\otimes$ in this context? The outer product? Then $u\otimes u$ would be a matrix and hence it wouldn't make sense to me to take the divergence of it.

Answer 1

Just searched in google and found this link $$\operatorname{div}(u\otimes v) = (\nabla u)v + (\operatorname{div}v)u.$$

Also, there is an explanation of your statement here using the notion of a tensor field.

I can't make out the meaning of this either, but it might help you...