Vortrag
Stability threshold of the 2D Couette flow in a homogeneous magnetic field
Vortrag von Dr. Michele Dolce
Sprecher eingeladen von: Prof. Dr. Klaus Widmayer
Datum: 26.10.23 Zeit: 16.15 - 18.00 Raum: ETH HG G 19.2
A planar incompressible and electrically conducting fluid can be described by the 2D Navier-Stokes-MHD system. One simple yet physically relevant laminar state is the Couette flow with a constant homogeneous magnetic field, given by \(u_E=(y,0)\), \(B_E=(b,0)\) in the domain \(\mathbb{T}\times\mathbb{R}\). The goal is to estimate how large can be a perturbation of this state while still resulting in a solution close to the laminar regime, thereby preventing the onset of turbulence. We prove that Sobolev regular initial perturbations of size \(O(Re^{-2/3})\), with Re being the Reynolds number, remain close to \(u_E, B_E\) and exhibit dissipation enhancement. The latter quantifies the convergence towards an x-independent state on a time-scale \(O(Re^{-1/3})\), much faster than the standard diffusive one \(O(Re^{-1})\).''