Fokker-Planck equation for dissipative 2D Euler equations with cylindrical noise
Probability
2021-08-11 v1
Abstract
After a short review of recent progresses in 2D Euler equations with random initial conditions and noise, some of the recent results are improved by exploiting a priori estimates on the associated infinite dimensional Fokker-Planck equation. The regularity class of solutions investigated here does not allow energy- or enstrophy-type estimates, but only bounds in probability with respect to suitable distributions of the initial conditions. This is a remarkable application of Fokker-Planck equations in infinite dimensions. Among the example of random initial conditions we consider Gibbsian measures based on renormalized kinetic energy.
Cite
@article{arxiv.1907.01994,
title = {Fokker-Planck equation for dissipative 2D Euler equations with cylindrical noise},
author = {Franco Flandoli and Francesco Grotto and Dejun Luo},
journal= {arXiv preprint arXiv:1907.01994},
year = {2021}
}
Comments
28 pages