Uniqueness results for the generators of the two-dimensional Euler and Navier-Stokes flows
The Euler and Navier-Stokes equations for an incompressible fluid in two dimensions with periodic boundary conditions are considered. Concerning the Euler equations, the associated (first order) Liouville operator \(L\) is considered as a symmetric linear operator in a Hilbert space \(L^2(\mu)\) with respect to a natural invariant Gaussian measure \(\mu\). For the Navier-Stokes equations with a suitable white noise forcing term the associated (second order) Kolmogorov operator \(K\) is considered. It is proved that both \(L\) and \(K\) are bounded by naturally positive Schrödinger-like operators. Some other uniqueness results for \(L\) and \(K\) are presented.
scientific article; zbMATH DE number 1836673
scientific article