Analyze discretely scale-invariant vorticity data

Investigate the dynamics and well-posedness of discretely scale-invariant vorticity data for the two-dimensional Euler equations in domains other than the previously studied symmetric settings.

Background

The paper studies scale-invariant vorticity in infinite sectors and notes that discretely scale-invariant data provide a natural broader class of nondecaying initial data. Such data satisfy a relation of the form f(x)=f(λx) for some λ>1, but need not be continuously scale-invariant. The authors identify the study of their dynamics as a possible extension of existing results on scale-invariant data, particularly because prior long-time analyses imposed strong rotational symmetry assumptions.

References

One possible direction is the study of discretely scale-invariant data, which we introduce in Subsection \ref{Bounded Vorticity} but, to the best of our knowledge, has not been investigated in the existing literature.

— Well-posedness threshold of the 2D Euler equations in Hölder spaces on infinite sectors  (2610.26315 - Choi, 19 Oct 2026) in Section 1, subsection “Scale-invariant data”