9 problems

Subcritical lifespan conjecture. If $1<p<p_0(n)$ with $n\geq3$, or $2<p<p_0(2)$ with $n=2$, then

Critical Strauss lifespan conjecture. The lifespan satisfies

The Intermediate Long Wave equation has small initial data of size $epsilon$ and dispersion relation … which is KdV-like at low frequencies and Benjamin–Ono-like at high frequencie…

Let $u$ solve the one-dimensional initial value problem … with compactly supported smooth initial data $u(x,0)=\varepsilon f(x)$ and $u_t(x,0)=\varepsilon g(x)$, where $p,q,r>1$,…

Let … denote the spherical water waves equation. Lifespan conjecture. If the Diophantine equation … , the lifespan goes beyond $\varepsilon^{-(1+\alpha)}$ as $\varepsilon\to0$. Fin…

Let a focusing flow satisfy the hypotheses of the paper, and let the result in Theorem provide its $epsilon^{-8}$ lifespan bound and accompanying estimates. Sharpness conjecture fo…

Let a one-dimensional dispersive flow on the real line have a cubic nonlinearity, and let its initial data have size $epsilon$ in a suitable Sobolev norm. Non-localized data focusi…

Critical-line conjecture. The critical line in the $(p,q)$-plane is given by

Let $T_{(Lifespan);\uplambda}$ denote the classical lifespan of the solution to the quasilinear wave equation with initial data…