ICTS:29941

Video URL

Yudovich theory for rough path perturbations of Euler’s equation - II

Yudovich theory for rough path perturbations of Euler’s equation - II

(2024). Yudovich theory for rough path perturbations of Euler’s equation - II. SciVideos. https://youtube.com/live/enqgoBXDRpA

Yudovich theory for rough path perturbations of Euler’s equation - II. SciVideos, Sep. 30, 2024, https://youtube.com/live/enqgoBXDRpA 

          @misc{ scivideos_ICTS:29941,
            doi = {},
            url = {https://youtube.com/live/enqgoBXDRpA},
            author = {},
            keywords = {},
            language = {en},
            title = {Yudovich theory for rough path perturbations of Euler{\textquoteright}s equation - II},
            publisher = {},
            year = {2024},
            month = {sep},
            note = {ICTS:29941 see, \url{https://scivideos.org/icts-tifr/29941}}
          }
Torstein Nilssen
Talk numberICTS:29941
Source RepositoryICTS-TIFR
Source EventDeterministic and Stochastic Analysis of Euler and Navier-Stokes Equations
Collection

Abstract

The lectures will introduce perturbations of Euler's equation by highly irregular paths where the perturbations are such that the solution preserves a range of physically relevant quantities. Using formal computations, we shall see that, when d=2, a purely Lagrangian formulation of the equation seems to be within reach.

However, special care is needed to give rigorous meaning to the noisy terms of the equation and in these lectures, we will consider the framework of rough paths. We will see how the so-called 'Sewing Lemma' can be used to define integrals as Riemann sums w.r.t paths of low regularity and how to use this result to construct rough path integrals. Then we will derive very precise a priori estimates for differential equations driven by rough paths and these estimates will be used to prove well-posedness of equations where the drift term satisfies an Osgood regularity. Moreover, we will study flows generated by the differential equations and see that the flows are volume ...