New bilinear estimates for quadratic-derivative nonlinear wave equations in 2+1 dimensions

New bilinear estimates for quadratic-derivative nonlinear wave equations in 2+1 dimensions

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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 n...

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Main Author: Tanguay, Allison J
Language:ENG
Published: ScholarWorks@UMass Amherst 2012
Subjects:
Mathematics
Online Access:https://scholarworks.umass.edu/dissertations/AAI3546060
id ndltd-UMASS-oai-scholarworks.umass.edu-dissertations-6686
record_format oai_dc
spelling ndltd-UMASS-oai-scholarworks.umass.edu-dissertations-66862020-12-02T14:32:54Z New bilinear estimates for quadratic-derivative nonlinear wave equations in 2+1 dimensions Tanguay, Allison J 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. 2012-01-01T08:00:00Z text https://scholarworks.umass.edu/dissertations/AAI3546060 Doctoral Dissertations Available from Proquest ENG ScholarWorks@UMass Amherst Mathematics
collection NDLTD
language ENG
sources NDLTD
topic Mathematics
spellingShingle Mathematics
Tanguay, Allison J
New bilinear estimates for quadratic-derivative nonlinear wave equations in 2+1 dimensions
description 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.
author Tanguay, Allison J
author_facet Tanguay, Allison J
author_sort Tanguay, Allison J
title New bilinear estimates for quadratic-derivative nonlinear wave equations in 2+1 dimensions
title_short New bilinear estimates for quadratic-derivative nonlinear wave equations in 2+1 dimensions
title_full New bilinear estimates for quadratic-derivative nonlinear wave equations in 2+1 dimensions
title_fullStr New bilinear estimates for quadratic-derivative nonlinear wave equations in 2+1 dimensions
title_full_unstemmed New bilinear estimates for quadratic-derivative nonlinear wave equations in 2+1 dimensions
title_sort new bilinear estimates for quadratic-derivative nonlinear wave equations in 2+1 dimensions
publisher ScholarWorks@UMass Amherst
publishDate 2012
url https://scholarworks.umass.edu/dissertations/AAI3546060
work_keys_str_mv AT tanguayallisonj newbilinearestimatesforquadraticderivativenonlinearwaveequationsin21dimensions
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