Q-Math Seminar
Random perturbations of flows and solutions of the Navier-Stokes equation
Speaker: Alberto Ibort (ICMAT-UC3M)Date: Thursday, 08 October 2026 - 14:00Place: Room 2.2.D08, Universidad Carlos III de Madrid
Abstract:
We show that solutions of the Navier-Stokes equation for an incompressible fluid can be obtained by averaging stochastic perturbations of solutions of Euler's equation. The average of a Brownian perturbation of a steady solution of the Euler equation defines, for small time, a time-dependent diffeomorphism whose generating vector field satisfies a generalized Navier-Stokes equation. The deviation of this generalized equation from the standard Navier-Stokes equation is controlled by a viscous residual whose leading term involves a transport--diffusion term. We identify a natural class of steady, parallel Euler flows for which this residual vanishes and the perturbed flow satisfies the exact Navier-Stokes equation. These results are placed in the context of recent developments including the stochastic Lagrangian representation of Constantin-Iyer, the SALT formulation of Holm, and regularization-by-noise results of Flandoli and collaborators.
