Global well-posedness of NLS equations
| dc.contributor | Graduate Program in Mathematics. | |
| dc.contributor.advisor | Gürel, Burak. | |
| dc.contributor.author | Yılmaz, Oğuz. | |
| dc.date.accessioned | 2023-10-15T11:13:22Z | |
| dc.date.available | 2023-10-15T11:13:22Z | |
| dc.date.issued | 2022 | |
| dc.description.abstract | The thesis is a survey of the I-method. After introducing the method, we discuss the implementation of this method to cubic, defocusing nonlinear Schrödinger equation in the spatial dimension n = 2 and quintic, defocusing nonlinear Schr¨odinger equation in the spatial dimension n = 1 with detailed calculations. We will find out on which type of equations one can use the I-method. We then mention our joint work with Engin Ba¸sako˘glu on the cubic defocusing fourth order nonlinear Schr¨odinger equation in the spatial dimension n = 4. Lastly, we discuss advantage and disadvantage of the method and share our idea of a study plan of the same equation in the spatial dimensions n = 2, 3 as future work. | |
| dc.format.pages | ix, 45 leaves | |
| dc.identifier.other | MATH 2022 Y56 | |
| dc.identifier.uri | https://digitalarchive.library.bogazici.edu.tr/handle/123456789/19901 | |
| dc.publisher | Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2022. | |
| dc.subject.lcsh | Schrödinger equation. | |
| dc.title | Global well-posedness of NLS equations |
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