Abstract/Details

A stochastic Lagrangian formulation of the incompressible Navier -Stokes and related *transport equations


2006 2006

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Abstract (summary)

In this dissertation we derive a representation of the deterministic 3-dimensional Navier-Stokes equations based on stochastic Lagrangian paths. The particle trajectories obey a stochastic differential equation with the (deterministic) velocity of the fluid as the drift, and a constant diffusion coefficient. We then recover the fluid's velocity field by using the inviscid Weber formula and averaging out the noise. We use this idea to provide formulations of related non-linear transport equations, including the viscous Burgers equations, Camassa-Holm and reaction diffusion equations.

We use the formulation above to provide a self contained local existence proof of the Navier-Stokes equations in spatially periodic domains. We conclude by examining a stochastic Lagrangian model where the particle trajectories obey a SDE where the drift is computed from the flow map without averaging. We show that the average of the velocity obtained from this system is a random translate of the Euler equations, and a super-linear approximation to the velocity field of the Navier-Stokes equations.

Indexing (details)


Subject
Mathematics
Classification
0405: Mathematics
Identifier / keyword
Pure sciences; Incompressible Navier-Stokes; Navier-Stokes equations; Stochastic Lagrangian; Transport
Title
A stochastic Lagrangian formulation of the incompressible Navier -Stokes and related *transport equations
Author
Iyer, Gautam
Number of pages
48
Publication year
2006
Degree date
2006
School code
0330
Source
DAI-B 67/05, Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
ISBN
9780542710490
Advisor
Constantin, Peter
University/institution
The University of Chicago
University location
United States -- Illinois
Degree
Ph.D.
Source type
Dissertations & Theses
Language
English
Document type
Dissertation/Thesis
Dissertation/thesis number
3219528
ProQuest document ID
304953924
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
Document URL
http://search.proquest.com/docview/304953924
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