We are concerned with the three-dimensional incompressible Navier–Stokes equations
driven by an additive stochastic forcing of trace class. First, for every divergence free initial …

We are concerned with the question of well‐posedness of stochastic, three‐dimensional,
incompressible Euler equations. In particular, we introduce a novel class of dissipative …

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 investigate a non-linear and non-local one dimensional transport equation
under random perturbations on the real line. We first establish a local-in-time theory, ie …

In this paper we establish a sharp nonuniqueness result for stochastic-dimensional ()
incompressible Navier–Stokes equations. First, for every divergence-free initial condition in …

In this paper we prove existence and uniqueness of local solutions to the three-dimensional
(3D) Navier–Stokes (N–S) equation driven by space–time white noise using two methods …

In this paper, we consider the noise effects on a class of stochastic evolution equations
including the stochastic Camassa–Holm equations with or without rotation. We first obtain …

We consider the stochastic Navier--Stokes equations in three dimensions and prove that the
law of analytically weak solutions is not unique. In particular, we focus on three examples of …

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 …

By using a regularity approximation argument, the global existence and uniqueness are
derived for a class of nonlinear SPDEs depending on both the whole history and the …