Conservation of total vorticity for a 2D stochastic Navier-Stokes equation
type: Item
instance of: scholarly article
title: Conservation of total vorticity for a 2D stochastic Navier-Stokes equation
zbMATH Open document ID: 1342.60097
DOI: 10.1155/2011/862186
author: Peter M. Kotelenez
author: Bradley T. Seadler
published in: Advances in Mathematical Physics
publication date: 2012-03-08T00:00:00Z
review text: Summary: We consider \(N\) point vortices whose positions satisfy a stochastic ordinary differential equation on \(\mathbb R^{2N}\) perturbed by spatially correlated Brownian noise. The associated signed point measure-valued empirical process turns out to be a weak solution to a stochastic Navier-Stokes equation (SNSE) with a state-dependent stochastic term. As the number of vortices tends to infinity, we obtain a smooth solution to the SNSE, and we prove the conservation of total vorticity in this continuum limit.
Mathematics Subject Classification ID: 60H15
Mathematics Subject Classification ID: 76D06
zbMATH DE Number: 6012972
Wikidata QID: Q58654864
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2011/862186
OpenAlex ID: W2053265914
cites work: A stochastic Navier-Stokes equation for the vorticity of a two-dimensional fluid
cites work: Hydrodynamics in two dimensions and vortex theory
cites work: Vortex theory approach to stochastic hydrodynamics
cites work: Large deviation principle for a stochastic Navier-Stokes equation in its vorticity form for a two-dimensional incompressible flow
cites work: Q3747436
cites work: Stochastic ordinary and stochastic partial differential equations. Transition from microscopic to macroscopic equations.
cites work: Macroscopic limits for stochastic partial differential equations of McKean-Vlasov type
cites work: Q3995021
cites work: Invariance principles in probability for triangular arrays of B-valued random vectors and some applications
cites work: On the Hahn-Jordan decomposition for signed measure valued stochastic partial differential equations
cites work: Q3914121
description: scientific article; zbMATH DE number 6012972