High Mode Transport Noise Improves Vorticity Blow Up Control in 3D

Explore a lecture on the regularizing effects of multiplicative transport noise on the vorticity form of 3D Navier-Stokes equations. Delve into the proof that stochastic transport noise provides a bound on vorticity, ensuring well-posedness with high probability. Examine the conditions of large noise intensity and high noise spectrum required for this result. Learn about the joint work of Dejun Luo and Franco Flandoli, presented as part of the Hausdorff Junior Trimester Program on Randomness, PDEs, and Nonlinear Fluctuations. Cover topics including nondegenerate additive noise in finite and infinite dimensions, NSEs with additive noise, transport noises for particle systems, stabilization by noise, and the scaling limit for stochastic 3D NSEs. Gain insights into Galerkin approximation, basic estimates, and the concepts of pathwise uniqueness and strong solutions in this 54-minute comprehensive exploration of high mode transport noise and vorticity blow up control in 3D.

Intro
Outline
Nondegenerate additive noise in finite dimensions
Extensions to infinite dimensions
NSEs with additive noise (cont.)
Transport noises for particle systems
Stabilization by noise
A trivial example
Some results in deterministic framework
Our model: 3D NSEs with transport noise
The transport noise
The final equation
Galerkin approximation and basic estimate
Scaling limit for stochastic 3D NSES
Some consequences
Pathwise uniqueness and strong solution