Journal of Nonlinear Mathematical Physics

Volume 17, Issue Supplement 1, March 2013, Pages 15 - 29

Solutions of Burgers, Reynolds, and Navier–Stokes Equations via Stochastic Perturbations of Inviscid Flows

Authors
Yuri E. Gliklikh
Mathematics Faculty, Voronezh State University, Universitetskaya pl. 1, Voronezh, 394006, Russia, yeg@math.vsu.ru, yeg2000@pisem.net
Received 12 January 2009, Accepted 31 May 2009, Available Online 7 January 2021.
DOI
https://doi.org/10.1142/S1402925110000775How to use a DOI?
Keywords
Group of diffeomorphisms, flat torus, stochastic perturbation, diffuse matter, Burgers equation, perfect incompressible fluid, Reynolds equation, Navier–Stokes equation
Abstract

We show that a certain stochastic perturbation of the flow of perfect incompressible fluid under some special external force on the flat n-dimensional torus yields a solution of Navier–Stokes equation without external force in the tangent space at unit of volume preserving diffeomorphism group. If that external force is absent, the equation turns into the one of Reynolds type. For the flow of diffuse matter this construction yields the Burgers equation.

Copyright
© 2010 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
17 - Supplement 1
Pages
15 - 29
Publication Date
2021/01
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.1142/S1402925110000775How to use a DOI?
Copyright
© 2010 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

TY  - JOUR
AU  - Yuri E. Gliklikh
PY  - 2021
DA  - 2021/01
TI  - Solutions of Burgers, Reynolds, and Navier–Stokes Equations via Stochastic Perturbations of Inviscid Flows
JO  - Journal of Nonlinear Mathematical Physics
SP  - 15
EP  - 29
VL  - 17
IS  - Supplement 1
SN  - 1776-0852
UR  - https://doi.org/10.1142/S1402925110000775
DO  - https://doi.org/10.1142/S1402925110000775
ID  - Gliklikh2021
ER  -