The classical continuation criterion makes integrated supremum vorticity a necessary divergence diagnostic at finite-time smooth breakdown.
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The classical continuation criterion makes integrated supremum vorticity a necessary divergence diagnostic at finite-time smooth breakdown.
Passage ID: euler-regularity:entry:bkm:v1
Source item: bkm
Source record: euler-regularity:source:bkm:v1
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Problem publication v9
Source assessment
Proved
Classical vorticity continuation criterion
Conditional necessary breakdown diagnostic, not construction of a singular solution.
Observed Oct 13, 2026
Scope
Finite-time smooth breakdown requires divergent integrated vorticity
Definition
Incompressible and unforced
History
A vorticity continuation criterion
Question
Three-dimensional Euler regularity
Further reading
Read the setting and notation before comparing the results.
Recorded authorship
J. Thomas Beale · Tosio Kato · Andrew Majda
J. Thomas Beale, Tosio Kato, Andrew Majda
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Remarks on the Breakdown of Smooth Solutions for the 3-D Euler Equations
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