- #1

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I have the following term in tensor notation

[tex] \frac{\partial{c}}{\partial{x_i}}\frac{\partial{u_i}}{\partial{x_j}}\frac{\partial{c}}{\partial{x_j}}[/tex]

I'm not sure how to write this in vector notation.

Would it be?

[tex]\nabla{c}\cdot\nabla\boldsymbol{u}\cdot{c}[/tex]

The problem I have is [tex]\nabla\boldsymbol{u}[/tex] is a tensor, whereas [tex]\nabla{c}[/tex] is a vector. Not sure what type of multiplication it would be between a vector and a tensor. Surely not a simple dot product?

Thanks.