Periodic nonlinear Schrödinger equation in critical H^s(\Tⁿ) spaces

2012/03/30 by Wang, Yuzhao
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1203.6738

Abstract

In this paper we prove some multi-linear Strichartz estimates for solutions to the linear Schrödinger equations on torus \Tⁿ. Then we apply it to get some local well-posed results for nonlinear Schrödinger equation in critical H^s(\Tⁿ) spaces. As by-products, the energy critical global well-posed results and energy subcritical global well-posed results with small initial data are also obtained.

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