We survey recent results in the mathematical literature on the equations of incompressible
fluid dynamics, highlighting common themes and how they might contribute to the …

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 …

In this paper, we consider the 2D incompressible Navier-Stokes equations on the torus. It is
well known that for any L 2 divergence-free initial data, there exists a global smooth solution …

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 review recent developments in the field of mathematical fluid dynamics which utilize
techniques that go under the umbrella name convex integration. In the hydrodynamical …

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

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

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∈ …

We show global existence and non-uniqueness of probabilistically strong, analytically weak
solutions of the three-dimensional Navier–Stokes equations perturbed by Stratonovich …

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 …