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Stability of 2D MHD with Only Horizontal Dissipation near a Background Magnetic Field on $\mathbb{R}^2$
Whether the two-dimensional Navier--Stokes equations with dissipation in only one direction are stable in $H^2$ on the whole plane is a well-known open problem: without transverse dissipation, a cubic interaction fails to be time-integrable. We show that a magnetic field removes this obstruction. Fo
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