3 papers
math.AP2025
Transition and Stability of 3D MHD Around Couette Flow
Niklas Knobel
We study the three-dimensional incompressible magnetohydrodynamic (MHD) equations near Couette flow with a constant magnetic field perpendicular to the shear plane. Couette flow in…
math.AP2025
Suppression of Fluid Echoes and Sobolev Stability Threshold for 2D Dissipative Fluid Equations Around Couette Flow
Niklas Knobel
We study the Sobolev stability thresholds of 2d dissipative fluid equations around Couette flow on the domain . We prove a bound for general nonlinear in…
math.AP2025
Ideal Magnetohydrodynamics Around Couette Flow: Long Time Stability and Vorticity-Current Instability
Niklas Knobel
This article considers the ideal 2D magnetohydrodynamic equations on an infinite periodic channel close to a combination of an affine shear flow, called Couette flow, and a constan…