Generic ill-posedness for Schrödinger equation with power-type nonlinearity on ${\mathbb{S}}^2$

Sijie Qian, Yilin Song, Ruixiao Zhang +1

In this article, we investigate the local well-posedness of the nonlinear Schrödinger equation on the two-dimensional sphere ${\mathbb{S}}^2$: \begin{align*} i\partial_tu+Δ_{g}u=F(…