Stability of energy-critical nonlinear Schrodinger equations in high dimensions
| dc.contributor.author | Tao, Terence | |
| dc.contributor.author | Visan, Monica | |
| dc.date.accessioned | 2021-06-22T17:35:49Z | |
| dc.date.available | 2021-06-22T17:35:49Z | |
| dc.date.issued | 2005-10-26 | |
| dc.description.abstract | We develop the existence, uniqueness, continuity, stability, and scattering theory for energy-critical nonlinear Schrödinger equations in dimensions n ≥ 3, for solutions which have larger, but finite, energy and large, but finite, Strichartz norms. For dimensions n ≤ 6, this theory is a standard extension of the small data well-posedness theory based on iteration in Strichartz spaces. However, in dimensions n > 6 there is an obstruction to this approach because of the subquadratic nature of the nonlinearity (which makes the derivative of the nonlinearity non-Lipschitz). We resolve this by iterating in exotic Strichartz spaces instead. The theory developed here will be applied in a subsequent paper of the second author, [21], to establish global well-posedness and scattering for the defocusing energy-critical equation for large energy data. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 28 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Tao, T., & Visan, M. (2005). Stability of energy-critical nonlinear Schrodinger equations in high dimensions. <i>Electronic Journal of Differential Equations, 2005</i>(118), pp. 1-28. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/13790 | |
| dc.language.iso | en | |
| dc.publisher | Texas State University-San Marcos, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2005, San Marcos, Texas: Texas State University-San Marcos and University of North Texas. | |
| dc.subject | Local well-posedness | |
| dc.subject | Uniform well-posedness | |
| dc.subject | Scattering theory | |
| dc.subject | Strichartz estimates | |
| dc.title | Stability of energy-critical nonlinear Schrodinger equations in high dimensions | |
| dc.type | Article |