3 problems

Dispersion conjecture. Localised smooth initial data satisfying the non-cavitation condition do not lead to stable structures localised in both spatial dimension. The solutions exi…

Let $F$ and $G$ be unimodal distributions in the sense that their quantile functions are differentiable almost everywhere, with derivatives $(F^{-1})'$ and $(G^{-1})'$ decreasing f…

Let $E\ll -1$. A large-negative-energy behavior conjecture asserts that the KdV soliton is stable under NV dynamics and that localized initial data will be radiated away to infinit…