Volume 17, Issue Supplement 1, December 2010, 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
- 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/).
Cite this article
TY - JOUR AU - Yuri E. Gliklikh PY - 2021 DA - 2021/01/07 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 - 10.1142/S1402925110000775 ID - Gliklikh2021 ER -