Global existence and non-uniqueness for 3D Navier–Stokes equations with space-time white noise
We establish that global-in-time existence and non-uniqueness of probabilistically strong
solutions to the three dimensional Navier–Stokes system driven by space-time white noise …
solutions to the three dimensional Navier–Stokes system driven by space-time white noise …
A class of supercritical/critical singular stochastic PDEs: existence, non-uniqueness, non-Gaussianity, non-unique ergodicity
We study the surface quasi-geostrophic equation with an irregular spatial perturbation∂ t θ+
u⋅∇ θ=− ν (− Δ) γ/2 θ+ ζ, u=∇⊥(− Δ)− 1 θ, on [0,∞)× T 2, with ν⩾ 0, γ∈[0, 3/2) and ζ∈ …
u⋅∇ θ=− ν (− Δ) γ/2 θ+ ζ, u=∇⊥(− Δ)− 1 θ, on [0,∞)× T 2, with ν⩾ 0, γ∈[0, 3/2) and ζ∈ …
Existence and uniqueness by Kraichnan noise for 2D Euler equations with unbounded vorticity
M Coghi, M Maurelli - arXiv preprint arXiv:2308.03216, 2023 - arxiv.org
We consider the 2D Euler equations on $\mathbb {R}^ 2$ in vorticity form, with unbounded
initial vorticity, perturbed by a suitable non-smooth Kraichnan transport noise. We show …
initial vorticity, perturbed by a suitable non-smooth Kraichnan transport noise. We show …
Weak coupling limit of the Anisotropic KPZ equation
We study the 2-dimensional anisotropic KPZ equation (AKPZ), which is formally given by∂
th= 1 2 Δ h+ λ ((∂ 1 h) 2−(∂ 2 h) 2)+ ξ, where ξ denotes a space-time white noise and λ> 0 …
th= 1 2 Δ h+ λ ((∂ 1 h) 2−(∂ 2 h) 2)+ ξ, where ξ denotes a space-time white noise and λ> 0 …
The stationary AKPZ equation: logarithmic superdiffusivity
G Cannizzaro, D Erhard… - Communications on Pure …, 2023 - Wiley Online Library
We study the two‐dimensional Anisotropic KPZ equation (AKPZ) formally given by∂ t H= 1 2
Δ H+ λ ((∂ 1 H) 2−(∂ 2 H) 2)+ ξ,* 3.4 pc ∂ _t H= 1 2 Δ H+ λ ((∂ _1 H)^ 2-(∂ _2 H)^ 2)+ ξ …
Δ H+ λ ((∂ 1 H) 2−(∂ 2 H) 2)+ ξ,* 3.4 pc ∂ _t H= 1 2 Δ H+ λ ((∂ _1 H)^ 2-(∂ _2 H)^ 2)+ ξ …
Fractional stochastic Landau-Lifshitz Navier-Stokes equations in dimension : Existence and (non-)triviality
R Jin, N Perkowski - arXiv preprint arXiv:2403.04911, 2024 - arxiv.org
We investigate fractional stochastic Navier-Stokes equations in $ d\ge 3$, driven by the
random force $(-\Delta)^{\frac {\theta}{2}}\xi $ which, as we show, corresponds to a fractional …
random force $(-\Delta)^{\frac {\theta}{2}}\xi $ which, as we show, corresponds to a fractional …
Brownian Particle in the Curl of 2-D Stochastic Heat Equations
G de Lima Feltes, H Weber - Journal of Statistical Physics, 2024 - Springer
We study the long time behaviour of a Brownian particle evolving in a dynamic random
environment. Recently, Cannizzaro et al.(Ann Probab 50 (6): 2475–2498, 2022) proved …
environment. Recently, Cannizzaro et al.(Ann Probab 50 (6): 2475–2498, 2022) proved …
Weak coupling limit of a Brownian particle in the curl of the 2D GFF
H Yang, Z Yang - arXiv preprint arXiv:2405.05778, 2024 - arxiv.org
In this article, we study the weak coupling limit of the following equation in $\mathbb {R}^ 2$:
$$ dX_t^\varepsilon=\frac {\hat {\lambda}}{\sqrt {\log\frac1\varepsilon}}\omega^\varepsilon …
$$ dX_t^\varepsilon=\frac {\hat {\lambda}}{\sqrt {\log\frac1\varepsilon}}\omega^\varepsilon …
Rough analysis and stochastic partial differential equations
R Jin - 2024 - ora.ox.ac.uk
Rough analysis involves the study of systems governed by (partial) differential equations
driven by irregular ('rough') signals. This thesis explores advancements in pathwise Itô …
driven by irregular ('rough') signals. This thesis explores advancements in pathwise Itô …