The role of smoothing effect in some dispersive equations
Name
1191254442-MIT.pdf
Size
1.14 MB
Format
Adobe PDF
Checksum (MD5)
6d795bd92aa7c93339509a9ce20683cd
Author(s)
Grande Izquierdo, Ricardo.
Advisor(s)
Gigliola Staÿlani.
Date Issued
2020
Publisher
Massachusetts Institute of Technology
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).
Subjects
Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
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.
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