3 papers
math.PR2026
Well-Posedness for SDEs with Logarithmical Critical Distributional Drifts
Zikai Chen, Zimo Hao, Xicheng Zhang
We study the stochastic differential equation on , where is a time-dependent, divergence-free distributional drift of critical…
math.AP2025
Harnack inequalities for nonlocal operators with supercritical drifts and their applications
Zhen-Qing Chen, Xicheng Zhang
In this paper, we investigate Harnack estimates for weak solutions to the following nonlocal equation: where denote…
math.PR2024
Distribution-flow dependent SDEs driven by (fractional) Brownian motion and Navier-Stokes equations
Zimo Hao, Michael Röckner, Xicheng Zhang
Motivated by the probabilistic representation for solutions of the Navier-Stokes equations, we introduce a novel class of stochastic differential equations that depend on the entir…