Rough Perturbations of the Navier Stokes System

Explore the intricate world of rough perturbations in the Navier-Stokes system through this 48-minute lecture by Torstein Nilssen. Delve into two distinct methods of perturbing the Navier-Stokes equation using rough paths, examining their physical relevance in terms of conserved quantities. Focus on defining intrinsic notions of solutions and corresponding well-posedness results. Journey through topics such as stochastic Navier-Stokes equations, energy methods for PDEs, rough path PDEs, unbounded rough drivers, a priori estimates, and the formulation of Navier-Stokes equations with constant coefficients. Investigate the importance of transport noise and vorticity in this context. Gain insights from this joint work with Martina Hofmanová and James-Michael Leahy, presented as part of the Hausdorff Junior Trimester Program on Randomness, PDEs, and Nonlinear Fluctuations at the Hausdorff Center for Mathematics.

Intro
Stochastic Navier-Stokes equations
Energy method for PDES
Rough path PDES
Unbounded rough drivers
A priori estimates
Back to the heat equation
Formulating Navier Stokes equation
Constant coefficients
Why transport noise?
Vorticity
Main results