3 problems

Critical-energy conjecture. The critical energy is exactly

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…