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Mathematical Research Letters
Volume 28 (2021)
Number 2
Probabilistic representation for mild solution of the Navier–Stokes equations
Pages: 563 – 573
DOI: https://dx.doi.org/10.4310/MRL.2021.v28.n2.a8
Author
Abstract
This paper is based on a formulation of the Navier–Stokes equations developed by Iyer and Constantin, where the velocity field of a viscous incompressible fluid is written as the expected value of a stochastic process. Our contribution is to establish this probabilistic representation formula for mild solutions of the Navier–Stokes equations on $\mathbb{R}^d$.
Christian Olivera is partially supported by FAPESP grants 2017/17670-0 and 2015/07278-0, and by CNPq grant 426747/2018-6.
Received 18 January 2019
Accepted 26 October 2019
Published 13 May 2021