On the nonlinear Schrödinger equation in spaces of infinite mass and low regularity

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