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Full-Text Articles in Physical Sciences and Mathematics
New Bilinear Estimates For Quadratic-Derivative Nonlinear Wave Equations In 2+1 Dimensions, Allison J. Tanguay
New Bilinear Estimates For Quadratic-Derivative Nonlinear Wave Equations In 2+1 Dimensions, Allison J. Tanguay
Open Access Dissertations
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.
Local Torsion On Abelian Surfaces, Adam Gamzon
Local Torsion On Abelian Surfaces, Adam Gamzon
Open Access Dissertations
Fix an integer d > 0. In 2008, Chantal David and Tom Weston showed that, on average, an elliptic curve over Q picks up a nontrivial p-torsion point defined over a finite extension K of the p-adics of degree at most d for only finitely many primes p. This dissertation is an extension of that work, investigating the frequency with which a principally polarized abelian surface A over Q with real multiplication by Q adjoin a squared-root of 5 has a nontrivial p-torsion point defined over K. Averaging by height, the main result shows that A …