English

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.

Keywords

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

R2 v1 2026-06-23T10:11:23.712Z