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October 1999 A Probabilistic Approach to the Two-Dimensional Navier-Stokes Equations
Barbara Busnello
Ann. Probab. 27(4): 1750-1780 (October 1999). DOI: 10.1214/aop/1022874814

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.

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Barbara Busnello. "A Probabilistic Approach to the Two-Dimensional Navier-Stokes Equations." Ann. Probab. 27 (4) 1750 - 1780, October 1999. https://doi.org/10.1214/aop/1022874814

Information

Published: October 1999
First available in Project Euclid: 31 May 2002

zbMATH: 0988.60057
MathSciNet: MR1742887
Digital Object Identifier: 10.1214/aop/1022874814

Subjects:
Primary: 60H10
Secondary: 35C15 , 35Q30 , 60J60 , 76D05

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

Rights: Copyright © 1999 Institute of Mathematical Statistics

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Vol.27 • No. 4 • October 1999
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