Second order perturbation theory of two-scale systems in fluid dynamics
A Debussche, U Pappalettera - Journal of the European Mathematical …, 2024 - ems.press
In the present paper we study fast-slow systems of coupled equations from fluid dynamics,
where the fast component is perturbed by additive noise. We prove that, under a suitable …
where the fast component is perturbed by additive noise. We prove that, under a suitable …
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∈ …
[HTML][HTML] Local existence and non-explosion of solutions for stochastic fractional partial differential equations driven by multiplicative noise
In this paper we prove the local existence and uniqueness of solutions for a class of
stochastic fractional partial differential equations driven by multiplicative noise. We also …
stochastic fractional partial differential equations driven by multiplicative noise. We also …
Maximal inequalities and exponential estimates for stochastic convolutions driven by Lévy-type processes in Banach spaces with application to stochastic quasi …
J Zhu, Z Brzeźniak, W Liu - SIAM Journal on Mathematical Analysis, 2019 - SIAM
We present remarkably simple proofs of Burkholder--Davis--Gundy inequalities for
stochastic integrals and maximal inequalities for stochastic convolutions in Banach spaces …
stochastic integrals and maximal inequalities for stochastic convolutions in Banach spaces …
[HTML][HTML] Restricted Markov uniqueness for the stochastic quantization of P (Φ) 2 and its applications
In this paper we obtain restricted Markov uniqueness of the generator and uniqueness of
martingale (probabilistically weak) solutions for the stochastic quantization problem in both …
martingale (probabilistically weak) solutions for the stochastic quantization problem in both …
Ergodicity for the stochastic quantization problems on the 2D-torus
In this paper we study the stochastic quantization problem on the two dimensional torus and
establish ergodicity for the solutions. Furthermore, we prove a characterization of the Φ^ 4_2 …
establish ergodicity for the solutions. Furthermore, we prove a characterization of the Φ^ 4_2 …
A general framework for solving singular SPDEs with applications to fluid models driven by pseudo-differential noise
H Tang, FY Wang - arXiv preprint arXiv:2208.08312, 2022 - arxiv.org
In this paper we focus on nonlinear SPDEs with singularities included in both drift and noise
coefficients, for which the Gelfand-triple argument developed for (local) monotone SPDEs …
coefficients, for which the Gelfand-triple argument developed for (local) monotone SPDEs …
Non-uniqueness in law of the two-dimensional surface quasi-geostrophic equations forced by random noise
K Yamazaki - arXiv preprint arXiv:2208.05673, 2022 - arxiv.org
Via probabilistic convex integration, we prove non-uniqueness in law of the two-dimensional
surface quasi-geostrophic equations forced by random noise of additive type. In its proof we …
surface quasi-geostrophic equations forced by random noise of additive type. In its proof we …
[HTML][HTML] Large deviation principles for the stochastic quasi-geostrophic equations
In this paper we establish the large deviation principle for the stochastic quasi-geostrophic
equation with small multiplicative noise in the subcritical case. The proof is mainly based on …
equation with small multiplicative noise in the subcritical case. The proof is mainly based on …
Invariant measures and global well posedness for the SQG equation
J Földes, M Sy - Archive for Rational Mechanics and Analysis, 2021 - Springer
We construct an invariant measure μ for the Surface Quasi-Geostrophic (SQG) equation and
show that almost all functions in the support of μ are initial conditions of global, unique …
show that almost all functions in the support of μ are initial conditions of global, unique …