Tensor products and correlation estimates with applications to nonlinear Schrödinger equations
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Bibliographic record
Abstract
Abstract We prove new interaction Morawetz‐type (correlation) estimates in one and two dimensions. In dimension 2 the estimate corresponds to the nonlinear diagonal analogue of Bourgain's bilinear refinement of Strichartz. For the two‐dimensional case we provide a proof in two different ways. First, we follow the original approach of Lin and Strauss but applied to tensor products of solutions. We then demonstrate the proof using commutator vector operators acting on the conservation laws of the equation. This method can be generalized to obtain correlation estimates in all dimensions. In one dimension we use the Gauss‐Weierstrass summability method acting on the conservation laws. We then apply the two‐dimensional estimate to nonlinear Schrödinger equations and derive a direct proof of Nakanishi's H 1 scattering result for every L 2 ‐supercritical nonlinearity. We also prove scattering below the energy space for a certain class of L 2 ‐supercritical equations. © 2009 Wiley Periodicals, Inc.
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Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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