%0 Journal Article
%T Strichartz estimates for partially periodic solutions to Schr£żdinger equations in 4d and applications
%A Sebastian Herr
%A Daniel Tataru
%A Nikolay Tzvetkov
%J Mathematics
%D 2010
%I arXiv
%R 10.1515/crelle-2012-0013
%X 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.
%U http://arxiv.org/abs/1011.0591v1