| Abstract: |
| We describe recent results on Kolmogorov and Fokker-Planck equations (transport and continuity equations in the deterministic case) associated mainly to 2D Euler equations with random initial conditions.
In the case of deterministic 2D Euler equations, we solve the Kolmogorov equation in a space of LlogL function (joint work with G. Da Prato and M. Roeckner). In the stochastic case, we mainly consider a transport type noise, which give rise to a moderately degenerate elliptic operator. We prove existence of solutions satisfying a suitable gradient estimate (joint work with D. Luo). We also investigate a special limit
from transport type noise with small space correlation to additive white noise. |
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