The role of smoothing effect in some dispersive equations
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, May, 2020
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| Formato: | Tesis |
| Lenguaje: | eng |
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Massachusetts Institute of Technology
2020
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| Acceso en línea: | https://hdl.handle.net/1721.1/126921 |
| _version_ | 1826192410917470208 |
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| author | Grande Izquierdo, Ricardo. |
| author2 | Gigliola Staÿlani. |
| author_facet | Gigliola Staÿlani. Grande Izquierdo, Ricardo. |
| author_sort | Grande Izquierdo, Ricardo. |
| collection | MIT |
| description | Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, May, 2020 |
| first_indexed | 2024-09-23T09:12:03Z |
| format | Thesis |
| id | mit-1721.1/126921 |
| institution | Massachusetts Institute of Technology |
| language | eng |
| last_indexed | 2024-09-23T09:12:03Z |
| publishDate | 2020 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/1269212020-09-04T03:40:15Z The role of smoothing effect in some dispersive equations Grande Izquierdo, Ricardo. Gigliola Staÿlani. Massachusetts Institute of Technology. Department of Mathematics. Massachusetts Institute of Technology. Department of Mathematics Mathematics. Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, May, 2020 Cataloged from the official PDF of thesis. Includes bibliographical references (pages 151-153). In this thesis, we study the role of smoothing effect in the local well-posedness theory of dispersive partial differential equations in three different contexts. First, we use it to overcome a loss of derivatives in a family of nonlocal dispersive equations. Second, we exploit a discrete version of the smoothing effect to study a discrete system of particles and how to approximate it by a continuous dispersive equation. Third, we use an anisotropic version of the smoothing effect to establish the local well-posedness theory of the two-dimensional Dysthe equation, which is used to model oceanic rogue waves. by Ricardo Grande Izquierdo. Ph. D. Ph.D. Massachusetts Institute of Technology, Department of Mathematics 2020-09-03T16:40:35Z 2020-09-03T16:40:35Z 2020 2020 Thesis https://hdl.handle.net/1721.1/126921 1191254442 eng MIT theses may be protected by copyright. Please reuse MIT thesis content according to the MIT Libraries Permissions Policy, which is available through the URL provided. http://dspace.mit.edu/handle/1721.1/7582 153 pages application/pdf Massachusetts Institute of Technology |
| spellingShingle | Mathematics. Grande Izquierdo, Ricardo. The role of smoothing effect in some dispersive equations |
| title | The role of smoothing effect in some dispersive equations |
| title_full | The role of smoothing effect in some dispersive equations |
| title_fullStr | The role of smoothing effect in some dispersive equations |
| title_full_unstemmed | The role of smoothing effect in some dispersive equations |
| title_short | The role of smoothing effect in some dispersive equations |
| title_sort | role of smoothing effect in some dispersive equations |
| topic | Mathematics. |
| url | https://hdl.handle.net/1721.1/126921 |
| work_keys_str_mv | AT grandeizquierdoricardo theroleofsmoothingeffectinsomedispersiveequations AT grandeizquierdoricardo roleofsmoothingeffectinsomedispersiveequations |