Question on partial derivative

1. Sep 18, 2008

Samoht

I just handed in a homework where I used the assumption below

iujjui=0 ?

but when I start thinking about it I'm not so sure, could someone prove to me that it is zero? Or is that assumption totally off?

Regards

2. Sep 18, 2008

CompuChip

Is there summation over i and j?
Is u something special, or just an arbitrary vector?

3. Sep 18, 2008

Samoht

This partial derivative came up in my proof that the rate of strain in fluid dynamics is always positive. u is the velocity and I believe that there is summation but I am very new at this.

The term I tried to prove being positive is:

iuj((∂iuj+∂jui)-2/3 ∂kuk δij)

When I multiply ∂iuj into the outer bracket then I get

(∂iuj(∂iuj+∂jui)-2/3 ∂kuk δijiuj)

which in my mind becomes

(∂iujiuj+∂iujjui)-2/3 ∂kuk δijiuj

the right side of the minus sign can be simplified to 2/3 (∂kuk)2

My question relates to the second term in the remaining bracket. Can the term ∂iujjui be set equal to 0? AND, if so why?

Regards