Date of Award

9-2012

Document Type

Open Access Dissertation

Degree Name

Doctor of Philosophy (PhD)

Degree Program

Mathematics

First Advisor

Andrea R. Nahmod

Second Advisor

Luc Rey-Bellet

Third Advisor

Rodolfo H. Torres

Subject Categories

Mathematics

Abstract

This thesis is concerned with the Cauchy problem for the quadratic derivative nonlinear wave equation in two spatial dimensions. Using standard techniques, we reduce local well-posedness in Fourier Lebesgue spaces to bilinear estimates in associated wave Fourier Lebesgue spaces, for which we prove new product estimates. These estimates then allow us to establish local well-posedness in a parameter range that gives improvement over previously known results on the Sobolev scale.

Included in

Mathematics Commons

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