Boltzmann equation

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The Boltzmann equation is given by (Ref.1 Eq 1 Chap. IX)

$\frac{\partial f_i}{\partial t} = - {\mathbf u}_i \cdot \frac{\partial f_i}{\partial {\mathbf r}} - {\mathbf F}_i \cdot \frac{\partial f_i}{\partial {\mathbf u}_i } + \sum_j C(f_i,f_j)$