4 problems

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 … 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…