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I'm considering to study some high-dimensional Navier-Stokes equations. One problem is to do write the viscous equation for vorticity, helicity and other conserved quantities. I think it might be better if it is possible to work with differential form and exterior calculus? Is there any reference that I may find somewhere?

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You mean in a form other than $\rho (\partial_t + v \cdot \nabla) v= f+ \dot{\overline \sigma}(\dot \nabla)$? Or formulas for the quantities you mention? –  Muphrid Dec 25 '12 at 22:09

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I refer to my book

Troy L. Story, Introduction to differential geometry with applications to Navier-Stokes dynamics.

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