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Dissertation/Thesis Abstract

Spherical averaged endpoint Strichartz estimates for the two-dimensional Schrödinger equations with inverse square potential
by Chen, I-Kun, Ph.D., University of Maryland, College Park, 2009, 72; 3372964
Abstract (Summary)

In this dissertation, I investigate the two-dimensional Schrödinger equation with repulsive inverse square potential, i.e., [special characters omitted] I prove the following version of the homogeneous endpoint Strichartz estimate: [special characters omitted] where the [special characters omitted] is a norm that takes L2 average in angular variable first and then supremum norm on radial variable, i.e., [special characters omitted]

The main result is presented in chapter 4. In chapter 2, I give a brief introduction on the equations that inspired my research, namely the Landau-Lifshitz equation and the Schrödinger map equation. In chapter 3, I introduce a geometric concept in order to obtain a gauge system suitable for analysis.

Indexing (document details)
Advisor: Grillakis, Manoussos G.
Commitee: Machedon, Matei, Margetis, Dionisios, Okoudjou, Kasso A., Weeks, John D.
School: University of Maryland, College Park
Department: Mathematics
School Location: United States -- Maryland
Source: DAI-B 70/09, Dissertation Abstracts International
Subjects: Mathematics
Keywords: Dispersive, Endpoints, Inverse square potentials, Partial differential equations, Schrodinger equations, Strichartz estimates
Publication Number: 3372964
ISBN: 978-1-109-38324-9
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