Strichartz estimates for partially periodic solutions to Schrodinger equations in 4d and applications

作者：Herr Sebastian^*; Tataru Daniel; Tzvetkov Nikolay

来源：Journal fur die Reine und Angewandte Mathematik, 2014, 690(690): 65-78.

DOI：10.1515/crelle-2012-0013

We consider the energy critical nonlinear Schrodinger equation on periodic domains of the form R-m x T4-m with m = 0, 1, 2, 3. Assuming that a certain L-4 Strichartz estimate holds for solutions to the corresponding linear Schrodinger equation, we prove that the nonlinear problem is locally well-posed in the energy space. Then we verify that the L-4 estimate holds if m = 2, 3.

• 出版日期2014-5