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Strichartz estimates for partially periodic solutions to Schrödinger equations in 4d and applications
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https://doi.org/10.1515/crelle-2012-0013Abstract
We consider the energy critical nonlinear Schrödinger equation on periodic domains of the form Rm × T4-m with m = 0,1, 2, 3. Assuming that a certain L4 Strichartz estimate holds for solutions to the corresponding linear Schrödinger equation, we prove that the nonlinear problem is locally well-posed in the energy space. Then we verify that the L4 estimate holds if m = 2, 3. © De Gruyter 2014.
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