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.
|Advisor:||Grillakis, Manoussos G.|
|Commitee:||Machedon, Matei, Margetis, Dionisios, Okoudjou, Kasso A., Weeks, John D.|
|School:||University of Maryland, College Park|
|School Location:||United States -- Maryland|
|Source:||DAI-B 70/09, Dissertation Abstracts International|
|Keywords:||Dispersive, Endpoints, Inverse square potentials, Partial differential equations, Schrodinger equations, Strichartz estimates|
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