Please use this identifier to cite or link to this item:
http://arks.princeton.edu/ark:/88435/dsp018s45qb99d
Title: | On the global solutions of quasilinear dispersive equations |
Authors: | Zhang, Yu |
Advisors: | Ionescu, Alexandru D |
Contributors: | Mathematics Department |
Subjects: | Mathematics |
Issue Date: | 2014 |
Publisher: | Princeton, NJ : Princeton University |
Abstract: | This thesis mainly focuses on certain nonlinear dispersive equations where the classical Picard's fix-point argument fails in obtaining the desired local or global solutions. More specifically, Chapter two proves the local well-posedness of the KP-I initial value problem on the torus T^2 with initial data in the Besov space B^1_{2,1} through a short-time estimate approach. Chapter three constructs global solutions to a modified ionic Euler-Poisson system in two dimensions, given the initial data is small smooth irrotational perturbation of the constant background. The main ingredients in the proof is a quasi-linear I-method approach, along with the Fourier transform method analyzing its space-time resonance feature. |
URI: | http://arks.princeton.edu/ark:/88435/dsp018s45qb99d |
Alternate format: | The Mudd Manuscript Library retains one bound copy of each dissertation. Search for these copies in the library's main catalog |
Type of Material: | Academic dissertations (Ph.D.) |
Language: | en |
Appears in Collections: | Mathematics |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
Zhang_princeton_0181D_11089.pdf | 477.97 kB | Adobe PDF | View/Download |
Items in Dataspace are protected by copyright, with all rights reserved, unless otherwise indicated.