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math.AP2026
A Hartman-Grobman Theorem for the Navier-Stokes Equation on
Rongchang Liu, Kening Lu, Lin Shi
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 for every . More prec…
math.AP2026
Spectral gap for the three-dimensional damped cubic wave equation with degenerate noise
Rongchang Liu, Kening Lu
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…
math.AP2026
Mixed Third-Order Flux Laws for Dual Cascade in the Stochastic SQG Equation
Rongchang Liu, Kening Lu, Zexin Wang
We study dual-cascade flux laws for the stochastic forced--dissipative surface quasi-geostrophic (SQG) equation on a large periodic box. For statistically stationary solutions, und…