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The moment equations

If one does not assume anything about the phase space distribution function $ P$, then the Maxwell equation (2.121) calculated for the velocity moments from zero to third ($ 1$, $ v_k$, $ v_k v_l$, $ v_k v_l v_h$) carries to the following set of equations [62,98]:

\begin{subequations}\begin{align}\frac{\partial (mn)}{\partial t} + \frac{\parti... ...cal{P}_{kl}\frac{\delta u_h}{\delta t} \end{split} \end{align}\end{subequations}

As it can be seen, the equation for the $ n-th$ moment contains the $ (n+1)-th$ moment. This means that some assumption must be introduced to close the Maxwell equations for the moments up to a given order.


Andrea Puglisi 2001-11-14