Strichartz estimates for Schrödinger equations on irrational tori in two and three dimensions

Abstract

In this paper, we prove new multilinear Strichartz estimates, which are obtained by using techniques of Bourgain. These estimates lead to new critical well-posedness results for the nonlinear Schrödinger equation on irrational tori in two and three dimensions with small initial data. In three dimensions, this includes the energy critical case. This extends recent work of Guo-Oh-Wang.

12 pages

Cited by in corpus (5)

• The Gross-Pitaevskii hierarchy on general rectangular tori
• Schrödinger equations on compact globally symmetric spaces
• The energy-critical nonlinear Schrödinger equation on a product of spheres
• Unconditional local well-posedness for periodic NLS
• Growth of higher Sobolev norms for energy critical NLS on irrational tori: small energy case