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

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

2010-11-02

arxiv.org/abs/1011.0591v1

Mathematics

Analysis of PDEs

15 pages

Scientific paper

We consider the energy critical nonlinear Schr\"odinger equation on periodic domains of the form R^m x T^{4-m} with m=0,1,2,3. Assuming that a certain L^4 Strichartz estimate holds for solutions to the corresponding linear Schr\"odinger 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, leaving open the cases m=0,1.

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