\(L^{1}\)-uniqueness of regularized 2D-Euler and stochastic Navier-Stokes equations
type: Item
instance of: scholarly article
title: \(L^{1}\)-uniqueness of regularized 2D-Euler and stochastic Navier-Stokes equations
zbMATH Open document ID: 1020.35071
DOI: 10.1016/S0022-1236(02)00182-9
author: Wilhelm Stannat
published in: Journal of Functional Analysis
publication date: 2003-05-25T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 47D07
Mathematics Subject Classification ID: 35R60
zbMATH DE Number: 1915622
zbMATH Keywords: 2D-Euler equation
zbMATH Keywords: measure-preserving flow
zbMATH Keywords: uniqueness
zbMATH Keywords: regularized stochastic 2D-Navier-Stokes equations
reviewed by: Stanisław Wedrychowicz
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1915622