# 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