7 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…

For a quasilinear wave equation whose nonlinearity has the form … and has a more favorable nonlinear structure, the associated local well-posedness should hold for Cauchy data with…

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…

Let $z_{2k+1}$ denote the $(k+1)$st order term in the higher-order expansion for the cubic nonlinear Schrödinger equation on $\mathbb{R}^3$. The original iterative procedure constr…

Optimal regularity conjecture. The optimal regularity is