The Annals of Probability

A Probabilistic Approach to the Two-Dimensional Navier-Stokes Equations

Barbara Busnello

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Abstract

We turn the Navier-Stokes equations for a 2-dimensional viscous incompressible fluid into a system of functional integrals in the trajectory space of a suitable diffusion process. Using probabilistic techniques as Girsanov’s transformation and Bismut-Elworthy formula, we prove the existence of a unique global solution of this system in a constructive way.

Article information

Source
Ann. Probab., Volume 27, Number 4 (1999), 1750-1780.

Dates
First available in Project Euclid: 31 May 2002

Permanent link to this document
https://projecteuclid.org/euclid.aop/1022874814

Digital Object Identifier
doi:10.1214/aop/1022874814

Mathematical Reviews number (MathSciNet)
MR1742887

Zentralblatt MATH identifier
0988.60057

Subjects
Primary: 60H10: Stochastic ordinary differential equations [See also 34F05]
Secondary: 76D05: Navier-Stokes equations [See also 35Q30] 60J60: Diffusion processes [See also 58J65] 35C15 35Q30: Navier-Stokes equations [See also 76D05, 76D07, 76N10]

Keywords
Navier-Stokes equations Functional integrals Stochastic differential equations Bismut-Elworthy formula Girsanov’s transformation

Citation

Busnello, Barbara. A Probabilistic Approach to the Two-Dimensional Navier-Stokes Equations. Ann. Probab. 27 (1999), no. 4, 1750--1780. doi:10.1214/aop/1022874814. https://projecteuclid.org/euclid.aop/1022874814


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References

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