Global existence and non-uniqueness of 3D Euler equations perturbed by transport noise
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 …
equations perturbed by Stratonovich transport noise. Kinetic energy of the solutions can be …
Global-in-time probabilistically strong and Markov solutions to stochastic 3D Navier–Stokes equations: existence and nonuniqueness
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 …
driven by an additive stochastic forcing of trace class. First, for every divergence free initial …
Non-unique ergodicity for deterministic and stochastic 3D Navier--Stokes and Euler equations
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 …
solutions to the three dimensional Navier--Stokes and Euler equations in the deterministic …
Weak well-posedness by transport noise for a class of 2D fluid dynamics equations
L Galeati, D Luo - arXiv preprint arXiv:2305.08761, 2023 - arxiv.org
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) …
equations with $(L^ 1_x\cap L^ p_x) $-valued vorticity are unique, for some $ p\in [1,\infty) …
A class of supercritical/critical singular stochastic PDEs: existence, non-uniqueness, non-Gaussianity, non-unique ergodicity
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∈ …
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∈ …
Global-in-time probabilistically strong solutions to stochastic power-law equations: existence and non-uniqueness
H Lü, X Zhu - Stochastic Processes and their Applications, 2023 - Elsevier
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 …
dimension d⩾ 3. For the power index r∈(1, 3 d+ 2 d+ 2), we establish existence of infinitely …
Nonuniqueness in law for stochastic hypodissipative Navier–Stokes equations
M Rehmeier, A Schenke - Nonlinear Analysis, 2023 - Elsevier
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 …
exponent 0< α< 1 2 on the three-dimensional torus perturbed by an additive Wiener noise …
Surface quasi-geostrophic equation perturbed by derivatives of space-time white 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 …
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 …
Non-uniqueness in law of three-dimensional magnetohydrodynamics system forced by random noise
K Yamazaki - Potential Analysis, 2024 - Springer
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 …
that is forced by random noise of an additive and a linear multiplicative type and has viscous …
Non-uniqueness in law of three-dimensional Navier–Stokes equations diffused via a fractional Laplacian with power less than one half
K Yamazaki - Stochastics and Partial Differential Equations: Analysis …, 2024 - Springer
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 …
by random noise, path-wise and more recently even in law, have been proven by various …