Global Well-posedness for Schrodinger Equations with Derivative in a Nonlinear Term and Data in Low-order Sobolev Spaces
| dc.contributor.author | Takaoka, Hideo | |
| dc.date.accessioned | 2020-06-09T21:15:49Z | |
| dc.date.available | 2020-06-09T21:15:49Z | |
| dc.date.issued | 2001-06-05 | |
| dc.description.abstract | In this paper, we study the existence of global solutions to Schrodinger equations in one space dimension with a derivative in a nonlinear term. For the Cauchy problem we assume that the data belongs to a Sobolev space weaker than the finite energy space H1. Global existence for H1 data follows from the local existence and the use of a conserved quantity. For Hs data with s < 1, the main idea is to use a conservation law and a frequency decomposition of the Cauchy data then follow the method introduced by Bourgain [3]. Our proof relies on a generalization of the tri-linear estimates associated with the Fourier restriction norm method used in [1, 25]. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 23 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Takaoka, H. (2001). Global well-posedness for Schrodinger equations with derivative in a nonlinear term and data in low-order Sobolev spaces. <i>Electronic Journal of Differential Equations, 2001</i>(42), pp. 1-23. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/11554 | |
| dc.language.iso | en | |
| dc.publisher | Southwest Texas State University, 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, 2001, San Marcos, Texas: Southwest Texas State University and University of North Texas. | |
| dc.subject | Nonlinear Schrodinger equation | |
| dc.subject | Well-posedness | |
| dc.title | Global Well-posedness for Schrodinger Equations with Derivative in a Nonlinear Term and Data in Low-order Sobolev Spaces | |
| dc.type | Article |