We construct Hölder continuous, global-in-time probabilistically strong solutions to 3D Euler
equations perturbed by Stratonovich transport noise. Kinetic energy of the solutions can be …

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 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 …

A fundamental open problem in fluid dynamics is whether solutions to $2 $ D Euler
equations with $(L^ 1_x\cap L^ p_x) $-valued vorticity are unique, for some $ p\in [1,\infty) …

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 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 …

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 …