\(L^{1}\)-uniqueness of regularized 2D-Euler and stochastic Navier-Stokes equations
A regularization of the 2D-Euler equation with periodic boundary conditions is introduced, having the same infinitesimal invariants as the Euler equation. A flow of measure-preserving transformations is constructed on \(L^1\)-spaces induced by the Gaussian measure with covariance given by the inverse of the enstrophy and it is shown that this flow is the only measure-preserving flow inducing a strongly continuous semigroup on the corresponding \(L^1\)-space. The author proves similar uniqueness results for a corresponding class of regularized stochastic 2D-Navier-Stokes equations.
regularized stochastic 2D-Navier-Stokes equations
scientific article; zbMATH DE number 1915622