Jia-Hao Xu

Global flows for the cubic nonlinear Schr\"odinger equation without decay assumptions

For each positive integer $N$, we construct global spectral group actions for the defocusing and focusing nonlinear Schr\"odinger hierarchies on initial-data classes containing $W^{2N+1,\infty}(\mathbb R)$. For $N\ge2$, the quadratic flow gives global classical cubic NLS solutions. The construction extends the Sato--Se...