5 papers
Navier-Stokes with a fractional transport noise as a limit of multi-scale dynamics
Xue-Mei Li, Szymon Sobczak
We define a bona fide rough path solution for the Navier-Stokes equation with an additional rough transport term, and show that the SPDE on the three-dimensional torus driven by a…
Strong completeness of SDEs and non-explosion for RDEs with coefficients having unbounded derivatives
Xue-Mei Li, Kexing Ying
We establish a non-explosion result for rough differential equations (RDEs) in which the noise and drift coefficients, together with their derivatives, may grow unboundedly at infi…
Fluctuations from a random fractional averaging limit
Xue-Mei Li, Colin Piernot, Szymon Sobczak +1
We consider a system of multiscale stochastic differential equations whose slow component is drivenby a fractional Brownian motion with Hurst parameter H greater than 1/2. Under er…
Stochastic nonlinear wave equation with rougher than white noise
Xue-Mei Li, Xianfeng Ren
We study the singular stochastic wave equation on , with a cubic nonlinearity and Gaussian rough Matérn forcing (a Fourier multiplier of order applied to space…
Coarse extrinsic curvature of Riemannian submanifolds
Marc Arnaudon, Xue-Mei Li, Benedikt Petko
We introduce a novel concept of coarse extrinsic curvature for Riemannian submanifolds, inspired by Ollivier's notion of coarse Ricci curvature. This curvature is derived from the…