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math.AP2024★ 2 cited
Sobolev Stability for the 2D MHD Equations in the Non-Resistive Limit
Niklas Knobel
In this article, we consider the stability of the 2D magnetohydrodynamics (MHD) equations close to a combination of Couette flow and a constant magnetic field. We consider the idea…
math.AP2023★ 3 cited
On the Sobolev Stability Threshold for the 2D MHD Equations with Horizontal Magnetic Dissipation
Niklas Knobel, Christian Zillinger
In this article we consider the stability threshold of the 2D magnetohydrodynamics (MHD) equations near a combination of Couette flow and large constant magnetic field. We study th…
math.AP2023
On Echoes in Magnetohydrodynamics with Magnetic Dissipation
Niklas Knobel, Christian Zillinger
We study the long time asymptotic behavior of the inviscid magnetohydrodynamic equations with magnetic dissipation near a combination of Couette flow and a constant magnetic field.…