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Multi-center vector field methods and some applications for dispersive equations
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Xiao, Jianguo. Multi-center vector field methods and some applications for dispersive equations. Retrieved from https://doi.org/doi:10.7282/T3SF2ZC0

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TitleMulti-center vector field methods and some applications for dispersive equations
NameXiao, Jianguo (author); Soffer, Avraham (chair); Tahvildar-Zadeh, Shadi Abdolre (internal member); Li, YanYan (internal member); Chen, Xuezhang (outside member); Rutgers University; Graduate School - New Brunswick
Date Created2016
Other Date2016-05 (degree)
SubjectMathematics, Wave equation
Extent1 online resource (vi, 61 p.)
DescriptionDecay estimates of various types have been widely used in studying the long time behavior of solutions to Dispersive Wave Equations. In this work, we develop the method of vector-fields to further study Dispersive Wave Equations. Radial vector fields are used to get a-priori estimates such as the Morawetz estimate on solutions of (nonlinear) Dispersive Wave Equations. A key to such estimates is the repulsiveness or nontrapping conditions on the flow corresponding to the wave equation. Thus this method is limited to potential perturbations which are repulsive, that is the radial derivative pointing away from the origin. In this work, we generalize this method to include potentials which are repulsive relative to a line in space (in three or higher dimensions), among other cases. This method is based on constructing multi-centered vector fields as multipliers, cancellation lemmas and energy localization.
NotePh.D.
NoteIncludes bibliographical references
Noteby Jianguo Xiao
Genretheses, ETD doctoral
Persistent URLhttps://doi.org/doi:10.7282/T3SF2ZC0
Languageeng
CollectionGraduate School - New Brunswick Electronic Theses and Dissertations
Organization NameRutgers, The State University of New Jersey
RightsThe author owns the copyright to this work.
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