Date of Award
9-2012
Document type
dissertation
Access 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.
DOI
https://doi.org/10.7275/3527631
Recommended Citation
Tanguay, Allison J., "New Bilinear Estimates for Quadratic-Derivative Nonlinear Wave Equations in 2+1 Dimensions" (2012). Open Access Dissertations. 625.
https://doi.org/10.7275/3527631
https://scholarworks.umass.edu/open_access_dissertations/625