• Corpus ID: 13942238

Solutions of equations of viscous hydrodynamics via stochastic perturbations of inviscid flows

@article{Gliklikh2009SolutionsOE,
  title={Solutions of equations of viscous hydrodynamics via stochastic perturbations of inviscid flows},
  author={Yuri E. Gliklikh},
  journal={arXiv: Analysis of PDEs},
  year={2009}
}
  • Y. Gliklikh
  • Published 6 August 2009
  • Mathematics
  • arXiv: Analysis of PDEs
We introduce a special stochastic perturbation of the flow of diffuse matter as a curve in the group of diffeomorphisms of flat n-dimensional torus such that the perturbed system yields a solution of Burgers equation in the tangent space at unit of the diffeomorphism group. The same perturbation of the flow of perfect incompressible fluid yields a solution of Reynolds type equation but under some special external force on the diffeomorphism group it transforms into a solution of Navier-Stokes… 

References

SHOWING 1-10 OF 15 REFERENCES

Groups of diffeomorphisms and the motion of an incompressible fluid

In this paper we are concerned with the manifold structure of certain groups of diffeomorphisms, and with the use of this structure to obtain sharp existence and uniqueness theorems for the classical

Ordinary and Stochastic Differential Geometry as a Tool for Mathematical Physics

Introduction. I. Elements of Coordinate-Free Differential Geometry. II. Introduction to Stochastic Analysis in Rn III. Stochastic Differential Equations on Manifolds. IV. Langevin's Equation in

Stochastic Analysis on Groups of Diffeomorphisms

Everywhere in this chapter we use the notions and notation introduced in Chapter 5. We describe a stochastic differential equation of a special sort on those groups of diffeomorphisms that arise in

Derivation of the Schrodinger equation from Newtonian mechanics

We examine the hypothesis that every particle of mass $m$ is subject to a Brownian motion with diffusion coefficient $\frac{\ensuremath{\hbar}}{2m}$ and no friction. The influence of an external

Sur la géométrie différentielle des groupes de Lie de dimension infinie et ses applications à l'hydrodynamique des fluides parfaits

© Annales de l’institut Fourier, 1966, tous droits réservés. L’accès aux archives de la revue « Annales de l’institut Fourier » (http://annalif.ujf-grenoble.fr/) implique l’accord avec les conditions

Global Analysis in Mathematical Physics: Geometric and Stochastic Methods

Introduction to Probability and Measure

According to a remark attributed to Mark Kac 'Probability Theory is a measure theory with a soul'. This book with its choice of proofs, remarks, examples and exercises has been prepared taking both

What are quantum fluctuations