High mode transport noise improves vorticity blow-up control in 3D Navier–Stokes equations
F Flandoli, D Luo - Probability Theory and Related Fields, 2021 - Springer
The paper is concerned with the problem of regularization by noise of 3D Navier–Stokes
equations. As opposed to several attempts made with additive noise which remained …
equations. As opposed to several attempts made with additive noise which remained …
Second order perturbation theory of two-scale systems in fluid dynamics
A Debussche, U Pappalettera - Journal of the European Mathematical …, 2024 - ems.press
In the present paper we study fast-slow systems of coupled equations from fluid dynamics,
where the fast component is perturbed by additive noise. We prove that, under a suitable …
where the fast component is perturbed by additive noise. We prove that, under a suitable …
Convex integration constructions in hydrodynamics
T Buckmaster, V Vicol - Bulletin of the American Mathematical Society, 2021 - ams.org
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 …
techniques that go under the umbrella name convex integration. In the hydrodynamical …
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 existence and non-uniqueness for 3D Navier–Stokes equations with space-time white noise
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 …
solutions to the three dimensional Navier–Stokes system driven by space-time white noise …
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 …
Uniqueness and non-uniqueness of the Gaussian free field evolution under the two-dimensional Wick ordered cubic wave equation
T Oh, M Okamoto, N Tzvetkov - Annales de l'Institut Henri Poincare …, 2024 - projecteuclid.org
We study the nonlinear wave equation (NLW) on the two-dimensional torus T 2 with
Gaussian random initial data on H s (T 2)× H s− 1 (T 2), s< 0, distributed according to the …
Gaussian random initial data on H s (T 2)× H s− 1 (T 2), s< 0, distributed according to the …
Scaling limit of stochastic 2D Euler equations with transport noises to the deterministic Navier–Stokes equations
F Flandoli, L Galeati, D Luo - Journal of Evolution Equations, 2021 - Springer
We consider a family of stochastic 2D Euler equations in vorticity form on the torus, with
transport-type noises and L^ 2 L 2-initial data. Under a suitable scaling of the noises, we …
transport-type noises and L^ 2 L 2-initial data. Under a suitable scaling of the noises, we …
On Ill‐and Well‐Posedness of Dissipative Martingale Solutions to Stochastic 3D Euler Equations
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 …
incompressible Euler equations. In particular, we introduce a novel class of dissipative …