The vorticity regularity threshold s=1+1/p separates existence of C^∞ compactly supported steady states and traveling waves near Couette flow from their non-existence in W^{s,p} and C^{1±} spaces.
Radial symmetry of stationary and uniformly-rotating solutions to the 2D Euler equation in a disc.preprint, 2024
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Flexibility and rigidity for the Couette flow in the infinite channel
The vorticity regularity threshold s=1+1/p separates existence of C^∞ compactly supported steady states and traveling waves near Couette flow from their non-existence in W^{s,p} and C^{1±} spaces.