Uniqueness results for the generators of the two-dimensional Euler and Navier-Stokes flows
type: Item
instance of: scholarly article
title: Uniqueness results for the generators of the two-dimensional Euler and Navier-Stokes flows
zbMATH Open document ID: 1034.35086
published in: Journal of Functional Analysis
publication date: 2002-11-28T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 76D05
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 35B10
Mathematics Subject Classification ID: 47D06
Mathematics Subject Classification ID: 47N20
zbMATH DE Number: 1836673
zbMATH Keywords: Euler and Navier-Stokes equations
zbMATH Keywords: invariant measures
zbMATH Keywords: Liouville and Kolmogorov generators
zbMATH Keywords: Navier-Stokes equations
zbMATH Keywords: white noise forcing term
zbMATH Keywords: uniqueness
author: S. Albeverio
author: Benedetta Ferrario
reviewed by: Il'ya Sh. Mogilevskii
MaRDI profile type: Publication
full work available at URL: jfan.2001.3927
OpenAlex ID: W2042804611
cites work: On uniqueness of invariant measures for finite- and infinite-dimensional diffusions
cites work: Global flows with invariant (Gibbs) measures for Euler and Navier-Stokes two dimensional fluids
cites work: 2D Vortex Motion of an Incompressible Ideal Fluid: The Koopman–von Neumann Approach
cites work: On the essential self-adjointness of Wick powers of relativistic fields and of fields unitary equivalent to random fields
cites work: Stochastic flows with stationary distribution for two-dimensional inviscid fluids
cites work: Q3747078
cites work: An approximate criterium of essential self-adjointness of Dirichlet operators
cites work: Dirichlet operators via stochastic analysis
cites work: Q4839117
cites work: Equilibrium states for a plane incompressible perfect fluid
cites work: Q4838903
cites work: On the statistical solutions of the two‐dimensional, periodic Euler equation
cites work: The two-dimensional Euler equation: A statistical study
cites work: Solutions et mesures invariantes pour des équations d'évolution stochastiques du type Navier-Stokes. (Solutions and invariant measures for stochastic evolution equations of the Navier-Stokes type)
cites work: Selfadjointness of some infinite-dimensional elliptic operators and application to stochastic quantization
cites work: Ergodicity for Infinite Dimensional Systems
cites work: Uniqueness and non-uniqueness of semigroups generated by singular diffusion operators
cites work: A Concise Presentation of the Euler Equations of Hydrodynamics
cites work: Ergodic results for stochastic navier-stokes equation
cites work: Stochastic Navier-Stokes equations: Analysis of the noise to have a unique invariant measure
cites work: Dissipativity and invariant measures for stochastic Navier-Stokes equations
cites work: Kolmogorov equation associated to a stochastic Navier-Stokes equation
cites work: Ergodicity of the 2-D Navier-Stokes equation under random perturbations
cites work: Q3910965
cites work: Q3870044
cites work: Q5815839
cites work: Q5526485
cites work: Q4705740
cites work: Selfadjointness of the Liouville operator for infinite classical systems
cites work: Semigroups of linear operators and applications to partial differential equations
cites work: Q5653193
cites work: Q4943987
cites work: Q3862204
cites work: Q3684480
cites work: An analytic approach to existence and uniqueness for martingale problems in infinite dimensions
DOI: 10.1006/JFAN.2001.3927
description: scientific article; zbMATH DE number 1836673