Boltzmann equation
The Boltzmann equation is given by (Ref.1 Eq 1 Chap. IX)
- Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle {\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})}
where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle } is an external force and the function C() represents binary collisions.