Smooth 2D Euler steady states with multiple critical points can be perturbed to make vorticity non-functional in the stream function, yielding isolated branches of stable states unlike the analytic case.
Shear flows of an ideal fluid and elliptic equations in unbounded domains.Comm
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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.
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On the flexibility of 2D Euler steady states
Smooth 2D Euler steady states with multiple critical points can be perturbed to make vorticity non-functional in the stream function, yielding isolated branches of stable states unlike the analytic case.
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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.