7 problems

Integral criterion conjecture. Small-data global existence holds if

Chen–Reissig's conjecture. If $C_{\mathrm{Str}}>0$, then the solution blows up at finite time for some initial data; if $C_{\mathrm{Str}}=0$, then small-data global existence holds…

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.…

Weak null conjecture. The original system of wave equations also admits global solutions for sufficiently small initial data.

Klein–Saut conjecture. The following assertions hold:

Let $u$ solve a quasilinear wave system of the form … with the weak null condition (WNC) defined by the existence of a global asymptotic-PDE solution for the ansatz … whose derivat…

Strauss's conjecture. If $p>p_1(n)$, then small-data solutions exist globally; if $1<p<p_1(n)$, then small-data solutions blow up in finite time.