3 problems

Finite-time breakdown conjecture for the b-equations. If, for some operator $A$, the Euler–Arnold equation has $C^1$ solutions that break down in finite time, then for every $b>1$…

McKean-type blowup conjecture. If

Critical-index conjecture. All solutions exist for all time if $k\geq \frac{n}{2}+1$, whereas for $k<\frac{n}{2}+1$ there are always some solutions that break down in finite time.…