167 citations · 730 across the 50 of their papers we have counts for
59 papers
Fluctuation dynamics in randomly advected Navier-Stokes equations below critical scaling
Arnaud Debussche, Martina Hofmanová
We study randomly advected incompressible Navier-Stokes equations, where the advecting field is a mean-zero, divergence-free, space-time stationary velocity field with smooth order…
Law of large numbers for stochastic multiscale spatial gene networks
Arnaud Debussche, Baptiste Huguet
We study a stochastic multiscale spatial gene network. These naturally arise in molecular biology. In our model, the reactants are subject to on-site reactions on both scales and d…
Preconditioning for the high-order sampling of the invariant distribution of parabolic semilinear SPDEs
Charles-Edouard Bréhier, Adrien Busnot Laurent, Arnaud Debussche +1
For a class of ergodic parabolic semilinear stochastic partial differential equations (SPDEs) with gradient structure, we introduce a preconditioning technique and design high-orde…
Periodic nonlinear Schrödinger equation with distributional potential and invariant measures
Arnaud Debussche, Antoine Mouzard
In this paper, we continue some investigations on the periodic NLSE started by Lebowitz, Rose and Speer and by Bourgain with the addition of a distributional multiplicative potenti…
Smoluchowski-Kramers diffusion approximation for systems of stochastic damped wave equations with non-constant friction
Sandra Cerrai, Arnaud Debussche
We consider systems of damped wave equations with a state-dependent damping coefficient and perturbed by a Gaussian multiplicative noise. Initially, we investigate their well-posed…
Rough analysis of two scale systems
Arnaud Debussche, Martina Hofmanová
We address a slow-fast system of coupled three dimensional Navier--Stokes equations where the fast component is perturbed by an additive Brownian noise. By means of the rough path…