By Vanessa Barros and others

We study the nonlinear Schr\"odinger equation with initial data in *\mathcal{Z}^s_p(\mathbb{R}^d)=\dot{H}^s(\mathbb{R}^d)\cap L^p(\mathbb{R}^d)*, where *0<s<\min\{d/2,1\}* and *2<p<2d/(d-2s)*. After showing that the linear Schr\"odinger group is well-defined in this space, we prove local well-posedness in the whole range of parameters *s* and *p*. The precise properties of the solution depend on the... Show more

November 6, 2020

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