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New bilinear estimates for quadratic-derivative nonlinear wave equations in 2+1 dimensions
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.
Subject Area
Mathematics
Recommended Citation
Tanguay, Allison J, "New bilinear estimates for quadratic-derivative nonlinear wave equations in 2+1 dimensions" (2012). Doctoral Dissertations Available from Proquest. AAI3546060.
https://scholarworks.umass.edu/dissertations/AAI3546060