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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 nonlinear Landau damping and Gevrey regularity
Christian Zillinger
In this article we study the problem of nonlinear Landau damping for the Vlasov-Poisson equations on the torus. As our main result we show that for perturbations initially of size…
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.…