Time integration of a variable over the domain

Hi,

I am solving a periodic fluid flow problem over a 2D domain. I need to find the time averaging of the term u*ux+u*vy at each point on the domain. I tried defining a global ODE but it gave an error saying that 'Failed to evaluate a variable Jacobian'. I am using version 4.2a. Please help me rexolve this issue!

Thanks,
Prashant