The role of smoothing effect in some dispersive equations
Author(s)Grande Izquierdo, Ricardo.
Massachusetts Institute of Technology. Department of Mathematics.
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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.
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, May, 2020Cataloged from the official PDF of thesis.Includes bibliographical references (pages 151-153).
DepartmentMassachusetts Institute of Technology. Department of Mathematics
Massachusetts Institute of Technology