# Homework Help: Verifying Fluid Dynamics Equation

1. Sep 16, 2008

### ICSunSpots

1. Verify that vjjvi=∂i(1/2*v2)-εijkvjωk,where ωkklmlvm

2. Relevant equations

3. The attempt at a solution
I am confused on how to proceed with this problem up to this point I have decomposed ωk into Curl(v). Which leaves vj X Curl(v). Decomposing this leaves vmivm-vllvi. I am stuck on where to go from here. How do I get rid of the ]=∂i(1/2*v2) term? Any help is appreciated. Thanks.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Sep 17, 2008

### tiny-tim

Welcome to PF!

Hi ICSunSpots! Welcome to PF!

Hint: ∂i(1/2*v2) = vjivj, isn't it?

3. Sep 17, 2008

### ICSunSpots

i(1/2*v2) = vjivj

Thank you for your reply. That would certainly make my solution thus far work.
However,
I am fairly new to index notation. Can you explain to me in vector notation what vjivj means? I understand the ]∂ivj term, but what does the vector vj in front of it do? Thanks.

4. Sep 17, 2008

### tiny-tim

I'm using the summation convention … repeated indices are added over all possible basis values.

So v2 = vjvj,

and so ∂iv2 = ∂i(vjvj) = (∂ivj)vj + vj(∂ivj) = 2vjivj

5. Sep 17, 2008

### ICSunSpots

Great! It's clear as day now. This index notation is really neat stuff, it just takes a little bit for it to be intuitive. Thank you for your help, I can now finish the problem.