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The role of smoothing effect in some dispersive equations

Author(s)
Grande Izquierdo, Ricardo.
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Other Contributors
Massachusetts Institute of Technology. Department of Mathematics.
Advisor
Gigliola Staÿlani.
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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
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Abstract
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.
Description
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).
 
Date issued
2020
URI
https://hdl.handle.net/1721.1/126921
Department
Massachusetts Institute of Technology. Department of Mathematics
Publisher
Massachusetts Institute of Technology
Keywords
Mathematics.

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