UNIFORM STRICHARTZ ESTIMATES ON THE LATTICE

초록

In this paper, we investigate Strichartz estimates for discrete linear Schrodinger and discrete linear Klein-Gordon equations on a lattice hZ(d) with h > 0, where h is the distance between two adjacent lattice points. As for fixed h > 0, Strichartz estimates for discrete Schrodinger and one-dimensional discrete Klein-Gordon equations are established by Stefanov-Kevrekidis [21]. Our main result shows that such inequalities hold uniformly in h is an element of (0, 1] with additional fractional derivatives on the right hand side. As an application, we obtain local well-posedness of a discrete nonlinear Schrodinger equation with a priori bounds independent of h. The theorems and the harmonic analysis tools developed in this paper would be useful in the study of the continuum limit h -> 0 for discrete models, including our forthcoming work [7] where strong convergence for a discrete nonlinear Schrodinger equation is addressed.

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