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arXiv · 1907.01994

Fokker-Planck equation for dissipative 2D Euler equations with cylindrical noise

Franco Flandoli·Francesco Grotto·Dejun Luo
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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.

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Franco Flandoli, Francesco Grotto, Dejun Luo. 2019-07-03. Fokker-Planck equation for dissipative 2D Euler equations with cylindrical noise. https://doi.org/10.1090/tpms%2F1130

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