| Abstract: |
| We consider the linear and nonlinear Schr\{o}dinger equations on the lattice $h\mathbb{Z}^d$, where $h$ is the (small) distance between two adjacent lattice points. For fixed h>0, it is known that weaker Strichartz estimates are available due to the lattice resonance. In this talk, we prove uniform (in h) Strichartz estimates with some loss of derivative, which is indeed necessary. As an applilcation, we obtain local well-posedness of the corresponding nonlinear problem with a uniform bound. |
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