Abstract
AbstractIn this note, we investigate the stability property of shear flows under the 2D stationary Navier–Stokes equations, and obtain that the Couette flow (y, 0) is stable under the space of for any and unstable in the space of , which is sharp in this sense. A key observation is the choice of the anisotropic cut‐off function. The Poiseuille flow (y2, 0) is also considered as a by‐product, which is stable in the space of with via a lemma of Fefferman–Stein.
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