Andrea R. NahmodLuc Rey-BelletRodolfo H. TorresTanguay, Allison J.2024-04-262024-04-262012-0910.7275/3527631https://hdl.handle.net/20.500.14394/39068This 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.Mathematicsdissertation