On stochastic Euler equations
type: Item
instance of: scholarly article
title: On stochastic Euler equations
zbMATH Open document ID: 0924.60047
DOI: 10.1007/BF02465554
author: G. Valiukevičius
author: R. Mikulevicius
published in: Lithuanian Mathematical Journal
publication date: 1999-11-14T00:00:00Z
review text: The authors consider equations for velocity fields describing compressible and incompressible motion of particles. The classical solutions for small time intervals are found. Next, the authors consider a uniform random perturbation of the position of individual particles \(X\) by a standard Brownian motion \(W\), i.e. \(\overline{X}(x,t)= X(x,t)+ \varepsilon W_t\). The velocity fields are solutions of the appropriate SPDE's (which are derived in the paper). It turns out that the limits, as \(\varepsilon \to 0\), are the deterministic velocity fields. For compressible motion a nonuniform random perturbation is considered.
Mathematics Subject Classification ID: 60H15
Mathematics Subject Classification ID: 35R60
zbMATH DE Number: 1262943
zbMATH Keywords: Euler equation
zbMATH Keywords: compressible and incompressible motion
zbMATH Keywords: random perturbation
reviewed by: Jacek Jakubowski
MaRDI profile type: Publication
cites work: Groups of diffeomorphisms and the motion of an incompressible fluid
cites work: Q4143915
cites work: Q4842675
cites work: Q5187597
cites work: Q3924932
cites work: Q3928750
full work available at URL: https://doi.org/10.1007/bf02465554
OpenAlex ID: W2077049771
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description: scientific article; zbMATH DE number 1262943