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I am currently reading the paper Global existence and scattering for rough solutions to generalized nonlinear Schrödinger equations on $\mathbb{R}$ by Colliander, Holmer, Visan, Zhang. In this article,...

Setting Although this detail is not relevant to my question, let me set the problem that my question arise. We are considering an initial value problem \begin{align*} \begin{cases} u\in L^\infty(I,H^{...