The role of smoothing effect in some dispersive equations
Author(s)
Grande Izquierdo, Ricardo.
Download1191254442-MIT.pdf (1.135Mb)
Other Contributors
Massachusetts Institute of Technology. Department of Mathematics.
Advisor
Gigliola Staÿlani.
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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
2020Department
Massachusetts Institute of Technology. Department of MathematicsPublisher
Massachusetts Institute of Technology
Keywords
Mathematics.