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Question on partial derivative

  1. Sep 18, 2008 #1
    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. jcsd
  3. Sep 18, 2008 #2

    CompuChip

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    Is there summation over i and j?
    Is u something special, or just an arbitrary vector?
     
  4. Sep 18, 2008 #3
    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
     
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