5 problems

Let $s$ denote the Sobolev regularity exponent in Theorem. Sharpness conjecture for the local well-posedness Sobolev range. The range of $s$ in Theorem is sharp for generic problem…

Let $s$ denote the Sobolev regularity exponent, and let Theorems and be the stated local well-posedness results for the two-dimensional and $n$-dimensional cubic problems. Large-da…

Let $s$ denote the Sobolev regularity exponent, and let Theorems and be the local well-posedness results stated in the source for the two-dimensional and $n$-dimensional cubic prob…

Let the cubic problems … be as in Theorem … also holds in the large-data case. The paper considers only small data, so this extension is stated as expected rather than proved here.

Consider the cubic problems denoted by … . Sharpness conjecture. Generically, the problem … is ill-posed in $H^s$ for $s<2$. The theorem establishes local well-posedness above thes…