We establish existence of infinitely many stationary solutions as well as ergodic stationary
solutions to the three dimensional Navier--Stokes and Euler equations in the deterministic …

We prove global in time well-posedness for perturbations of the 2D stochastic Navier–
Stokes equations∂ tu+ u·∇ u= Δ u-∇ p+ ζ+ ξ, u (0,·)= u 0, div (u)= 0, driven by additive …

The goal of the present paper is to establish a framework which allows to rigorously
determine the large-scale Gaussian fluctuations for a class of singular SPDEs at and above …

We are concerned with the power-law fluids driven by an additive stochastic forcing in
dimension d⩾ 3. For the power index r∈(1, 3 d+ 2 d+ 2), we establish existence of infinitely …

We study the incompressible hypodissipative Navier–Stokes equations with dissipation
exponent 0< α< 1 2 on the three-dimensional torus perturbed by an additive Wiener noise …

We consider a family of singular surface quasi-geostrophic equations∂ tθ+ u·∇ θ=− ν (−)
γ/2θ+(−) α/2ξ, u=∇⊥(−)− 1/2θ, on [0,∞)× T2, where ν⩾ 0, γ∈[0, 3/2), α∈[0, 1/4) and ξ is a …

We prove non-uniqueness in law of the three-dimensional magnetohydrodynamics system
that is forced by random noise of an additive and a linear multiplicative type and has viscous …

We study well-posedness for the stochastic transport equation with transport noise, as
introduced by Flandoli, Gubinelli, and Priola [Invent. Math., 180 (2010), pp. 1–53]. We …

Non-uniqueness of three-dimensional Euler equations and Navier-Stokes equations forced
by random noise, path-wise and more recently even in law, have been proven by various …

We consider a transport-diffusion equation forced by random noise of three types: additive,
linear multiplicative in Itô's interpretation, and transport in Stratonovich's interpretation. Via …