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.
Metastability of Kolmogorov flows and inviscid damping of shear flows.Arch
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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.