Date of Award
Doctor of Philosophy (PhD)
Andrea R. Nahmod
Rodolfo H. Torres
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.
Tanguay, Allison J., "New Bilinear Estimates for Quadratic-Derivative Nonlinear Wave Equations in 2+1 Dimensions" (2012). Open Access Dissertations. Paper 625.