Mathematical Research Letters

Volume 28 (2021)

Number 2

Probabilistic representation for mild solution of the Navier–Stokes equations

Pages: 563 – 573



Christian Olivera (Departamento de Matemática, Universidade Estadual de Campinas, S.P., Brazil)


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