ICTS:29917

Video URL

Regularization by noise - IV

Regularization by noise - IV

(2024). Regularization by noise - IV. SciVideos. https://youtube.com/live/sxQiiKcAym8

Regularization by noise - IV. SciVideos, Sep. 26, 2024, https://youtube.com/live/sxQiiKcAym8 

          @misc{ scivideos_ICTS:29917,
            doi = {},
            url = {https://youtube.com/live/sxQiiKcAym8},
            author = {},
            keywords = {},
            language = {en},
            title = {Regularization by noise - IV},
            publisher = {},
            year = {2024},
            month = {sep},
            note = {ICTS:29917 see, \url{https://scivideos.org/icts-tifr/29917}}
          }
Mario Maurelli
Talk numberICTS:29917
Source RepositoryICTS-TIFR
Source EventDeterministic and Stochastic Analysis of Euler and Navier-Stokes Equations
Collection

Abstract

We say that an ordinary or partial differential equation is regularized by noise if the addition of a suitable noise term restores well-posedness or improves regularity of the solution to the equation. Regularization by noise is by now well understood for ODEs and linear transport-type PDEs, but it is less understood for nonlinear PDEs like Euler and Navier-Stokes equations, with many open questions.

In the first part of this series of lectures, we consider the case of ODEs and associated transport equations with irregular drift: we show that the addition of an additive Brownian noise restores well-posedness of the ODE; we introduce the corresponding transport noise and show that this noise restores well-posedness for the associated transport equation. In the second part, we focus our attention on the effect of a particular transport-type noise, which is divergence-free, Gaussian, white in time and poorly correlated in space (nonsmooth Kraichnan noise). The associated linear transpo...