DOI link for Transport Equations
Transport Equations book
Let us define the averaging procedure of an arbitrary value 'Pa (va, r, t) with the help of the distribution function /a (va, r, t)
na ('Pa} =I 'Pafadv. (2.1.2) The left-hand side of (2.1.1) can be transformed using the relations
30 Clw.pter f. 7hm~port equatiom
The latter expression is written only for one of the Cartesian components. In (2.1.5} the first term resulting from the integration by part vanishes as it is assumed that 1/Ja/a - 0 at Vz - oo and Vz - -oo. Besides, it is implied that for the external force of (1.2.19} the condition oFa~/&at = 0 is valid. For the constituent of Fa which is velocity-dependent (the Lorentz force) this requirement is met because the Cartesian l-component of the vector product does not include the lth component of the particle velocity.