Almost-sure enhanced dissipation and uniform-in-diffusivity exponential mixing for advection–diffusion by stochastic Navier–Stokes
J Bedrossian, A Blumenthal… - Probability Theory and …, 2021 - Springer
We study the mixing and dissipation properties of the advection–diffusion equation with
diffusivity 0< κ ≪ 1 0< κ≪ 1 and advection by a class of random velocity fields on T^ d T d …
diffusivity 0< κ ≪ 1 0< κ≪ 1 and advection by a class of random velocity fields on T^ d T d …
The Batchelor spectrum of passive scalar turbulence in stochastic fluid mechanics at fixed Reynolds number
J Bedrossian, A Blumenthal… - … on Pure and Applied …, 2022 - Wiley Online Library
In 1959 Batchelor predicted that the stationary statistics of passive scalars advected in fluids
with small diffusivity k should display a power spectrum along an inertial range contained in …
with small diffusivity k should display a power spectrum along an inertial range contained in …
The Batchelor spectrum of passive scalar turbulence in stochastic fluid mechanics at fixed Reynolds number
J Bedrossian, A Blumenthal… - arXiv preprint arXiv …, 2019 - arxiv.org
In 1959, Batchelor predicted that the stationary statistics of passive scalars advected in fluids
with small diffusivity $\kappa $ should display a $| k|^{-1} $ power spectrum along an inertial …
with small diffusivity $\kappa $ should display a $| k|^{-1} $ power spectrum along an inertial …
On the chaotic behavior of the Lagrangian flow of the 2D Navier-Stokes system with bounded degenerate noise
V Nersesyan, D Zhang, C Zhou - arXiv preprint arXiv:2406.17612, 2024 - arxiv.org
We consider a fluid governed by the randomly forced 2D Navier-Stokes system. It is
assumed that the force is bounded, acts directly only on a small number of Fourier modes …
assumed that the force is bounded, acts directly only on a small number of Fourier modes …
Lagrangian chaos and scalar advection in stochastic fluid mechanics
J Bedrossian, A Blumenthal… - Journal of the European …, 2022 - ems.press
We study the Lagrangian flow associated to velocity fields arising from various models of
stochastic fluid mechanics. We prove that in many circumstances, these flows are chaotic …
stochastic fluid mechanics. We prove that in many circumstances, these flows are chaotic …
Irreducibility of SPDEs driven by pure jump noise
The irreducibility is fundamental for the study of ergodicity of stochastic dynamical systems.
In the literature, there are very few results on the irreducibility of stochastic partial differential …
In the literature, there are very few results on the irreducibility of stochastic partial differential …
Local large deviations for randomly forced nonlinear wave equations with localized damping
Y Chen, Z Liu, S Xiang, Z Zhang - arXiv preprint arXiv:2409.11717, 2024 - arxiv.org
We study the large deviation principle (LDP) for locally damped nonlinear wave equations
perturbed by a bounded noise. When the noise is sufficiently non-degenerate, we establish …
perturbed by a bounded noise. When the noise is sufficiently non-degenerate, we establish …
Large deviations principle via Malliavin calculus for the Navier–Stokes system driven by a degenerate white-in-time noise
The purpose of this paper is to establish the Donsker–Varadhan type large deviations
principle (LDP) for the two-dimensional stochastic Navier–Stokes system. The main novelty …
principle (LDP) for the two-dimensional stochastic Navier–Stokes system. The main novelty …
Observable full-horseshoes for Lagrangian flows advected by stochastic 2D Navier-Stokes equations
W Huang, J Zhang - arXiv preprint arXiv:2311.05193, 2023 - arxiv.org
In this paper, we mainly study the turbulence of Lagrangian flow advected by stochastic 2D
Navier-Stokes equations. It is proved that this system has observable full-horseshoes. The …
Navier-Stokes equations. It is proved that this system has observable full-horseshoes. The …
A detailed fluctuation theorem for heat fluxes in harmonic networks out of thermal equilibrium
M Damak, M Hammami, CA Pillet - Journal of Statistical Physics, 2020 - Springer
We continue the investigation, started in Jakšić et al. in (J. Stat. Phys. 166: 926–1015, 2017),
of a network of harmonic oscillators driven out of thermal equilibrium by heat reservoirs. We …
of a network of harmonic oscillators driven out of thermal equilibrium by heat reservoirs. We …