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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.

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3: Liouville equation for N = 3 particles

2:D₂(f₂) = J₂(f₃)

⇒

with tertiary molecular chaos

(Tsugé equation)

with

(Kármán-Howarth equation)

1:D(f) = J(f₂)

where D denotes differential operator, and J is the collision integral operator.

⇒

(Reynolds averaged Navier-Stokes equation)