Periodic nonlinear Schrödinger equation in critical \(H^{s}(\mathbb{T}^n)\) spaces. (English) Zbl 1291.35369
Summary: In this paper we prove some multilinear Strichartz estimates for solutions to the linear Schrödinger equation on the torus \(\mathbb{T}^n\). Then we apply them to get some well-posedness results for the periodic nonlinear Schrödinger equation in critical \(H^{s}(\mathbb{T}^n)\) spaces.
MSC:
35Q55 | NLS equations (nonlinear Schrödinger equations) |