In a seminal work, Leray (1934) demonstrated the existence of global weak solutions to the
Navier-Stokes equations in three dimensions. We exhibit two distinct Leray solutions with …

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 …

For any regularity exponent β< 1 2, we construct non-conservative weak solutions to the 3D
incompressible Euler equations in the class C t 0 (H β∩ L 1 (1-2 β)). By interpolation, such …

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 …

We consider the homogeneous incompressible Euler equations∂ tv+ div (v⊗ v)+∇ p= 0(1.1
a) div v= 0(1.1 b) for the unknown velocity vector field v and scalar pressure field p, posed on …

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 …

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 …

The aim of this book is to provide beginning graduate students who completed the first two
semesters of graduate-level analysis and PDE courses with a first exposure to the …

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 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∈ …