Claim: The pressure $p$ can be interpreted as Lagarange multiplicator that comes from incompressibility constraint $\nabla \cdot u=0$.
Basis: Lagrange multiplicator are associated to variational problem.
Problem: Navier-Stokes equation has no variational structure.
Alternative: Consider special cases: Stokes and Euler equation, which have a variational structure.
Let 
, a sequence 
converges weakly to 
if
Let us seek for solutions of 
satisfying the scaling hypothesis
and 
are reparametrization of time and 
. The prefactor 
ensures that 
conserves mass, i.e.
The Fokker Planck equation has the form
is a smooth function, 
some parameter and 
a probability density on 
. The partial differential equation is in divergence form and conserves mass. Hence, also 
is a probability density on . In the case, where 
has some growth at 
, the equilibrium solutions 
are characterized by
