We prove a local Hartman-Grobman theorem at zero for the unforced Navier-Stokes equation on the three-dimensional torus in the strong topology of $H^s$ for every $s>7/2$. More precisely, we construct a homeomorphism between open positively invariant neighborhoods of zero that conjugates the Navier-Stokes semiflow to th...
We prove polynomial mixing for the defocusing damped cubic stochastic nonlinear Schr\"odinger equation on the three-dimensional torus under saturating smooth finite rank Brownian forcing. The mixing rate is measured in the $p$-Wasserstein metric induced by the $H^1$ distance for every $1\le p<\infty$. We also obtain sh...
We prove a weighted Wasserstein spectral gap for the three-dimensional primitive equations on $\mathscr E=\{u\in H^1\cap L^8: \partial_zu\in L^4\}$ under finite-rank additive Brownian forcing that is phase-complete finite Fourier and satisfies a quantitative quadratic saturation condition. In particular, four real forc...
We prove unique ergodicity of the projective process associated with the two dimensional Navier--Stokes equation in vorticity form, with additive diagonal noise acting on every nonzero real Fourier phase and satisfying two sided power law bounds. Consequently, the exact Furstenberg--Khasminskii formula for the top Lyap...
We establish a weighted Wasserstein spectral gap for the three-dimensional damped cubic wave equation with genuinely finite rank Brownian forcing. Under a saturation condition, the gap holds with respect to the negative phase topology $\mathcal E_s=H^{-s}\times H^{-1-s}$ for every $0<s<1/2$, from which we deduce unique...
Rong-Chang Liu, Ke-Ning Lu· 1 citation
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