Passive Advection and the Degenerate Elliptic Operators $M_n$
  We prove estimates for the stationary state $n$-point functions at zero molecular diffusivity in the Kraichnan model. This is done by proving upper bounds for the heat kernels and Green's functions of the degenerate elliptic operators $M_n$ that occur in the Hopf equations for the $n$-point functions. 
Ville Hakulinen