6 problems

Critical-exponent conjecture. The critical exponent of the equation is

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…

Stability and quenching-profile conjecture. The following statements are conjectured:

Forbidden mass interval conjecture. The interval

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.