Kinetic Theory  Fluid Mechanics 
N: Liouville equation for N particles 

N ‒ 1: Liouville equation for N ‒ 1 particles 

N ‒ 2: Liouville equation for N ‒ 2 particles 

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3: Liouville equation for N = 3 particles 

2:D_{2}(f_{2}) = J_{2}(f_{3})  ⇒ 
with tertiary molecular chaos (Tsugé equation)  with (KármánHowarth equation) 
1:D(f) = J(f_{2}) where D denotes differential operator, and J is the collision integral operator.  ⇒ (Reynolds averaged NavierStokes equation) 