Strichartz estimates for partially periodic solutions to Schr
By Sebastian Herr, D. Tataru, Nikolay Tzvetkov. 2010
99 citations recorded by the source corpus.
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.
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/8a2d6b009520060c8f8cad0a34093cda9aeb76a3
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In Applied Mathematics
- Tadahiro Oh
- Nicola Visciglia
- Nikolay Tzvetkov
- Zihua Guo
- Yuzhao Wang
- Benoit Pausader
- Zaher Hani
- Gigliola Staffilani
In Mathematical Physics
- Tadahiro Oh
- Nicola Visciglia
- Benoit Pausader
- Nikolay Tzvetkov
- Zihua Guo
- Yuzhao Wang
- Zaher Hani
- Gigliola Staffilani
Citations in the corpus
- Strichartz estimates for Schrödinger equations on irrational tori (2013, methodology): “Furthermore, by applying the well-posedness theory involving the U- and V -spaces developed by Tataru, Koch, and their collaborators [18, 21, 22, 30], we prove some critical local well-posedness.”
- MODIFIED SCATTERING FOR THE CUBIC SCHRÖDINGER EQUATION ON PRODUCT SPACES AND APPLICATIONS (2013, background): “In light of the above sharp contrast in behavior between Rd and its compact quotient Td, considerable interest has emerged in the past few years to study questions of long-time behavior on “in between” manifolds, like the ones presented by the non-compact quotients of Euclidean space [52, 59, 60, 84”