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 …

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∈ …

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 …

We present remarkably simple proofs of Burkholder--Davis--Gundy inequalities for
stochastic integrals and maximal inequalities for stochastic convolutions in Banach spaces …

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 …

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 …

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 …

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 …

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 …

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 …