Cartan methods and Solutions to Navier-Stokes equations

By multipying the Navier Stokes equations by the vector of differential displacement and then by rearranging terms, it becomes apparent that the Navier Stokes equations are a constraint on a vector field f constructed from algebraic combinations of the derivatives of the fluid velocity vector v, such that the vector f satisfies the Frobenius integrability theorem. In other words the vector f can be expressed in terms of two independent functions at most. Using this constraint of "two dimensionality" it is possible to derive a constraint equation whose solution is simpler than that of the original Navier Stokes equations. Once the constraint solution is found, the rest of the Navier Stokes solution is found by quadratures.


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Last update 01/23/2009
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