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What is known about (3D) steady incompressible Euler flows with compact support?

(Looking for results in a field you are not familiar with sure is tough. I had a hope to find clues starting from the famous paper of V. Scheffer about a flow with compact support in space-time, and from works on vortex rings I could find, but in both cases ended up empty handed. This problem was considered by some, I presume? )

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According to the following paper, it is an open problem whether such solutions exist: N. Nadirashvili, Liouville theorem for Beltrami flow, Geometric and Functional Analysis 24 (2014), 916-921.

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  • $\begingroup$ Thank you. I have two problems with this source though: 1. There is no reference at all. 2. The space is not mentioned (no solution even in $L^2$?) $\endgroup$ – Alex Gavrilov Mar 1 '18 at 5:22
  • $\begingroup$ @AlexGavrilov: How would you give a reference to substantiate that a problem is open? I mean, other than by citing someone else who has made the same statement. $\endgroup$ – Michael Renardy Mar 1 '18 at 18:04
  • $\begingroup$ I simply suspect that the problem is open but very obscure and not interesting to anyone besides a couple of experts. Actually, I had plans to try and construct an example, but given the response I am about to change my mind. $\endgroup$ – Alex Gavrilov Mar 2 '18 at 12:00

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